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source: downloads/boost_1_33_1/boost/math/octonion.hpp @ 12

Last change on this file since 12 was 12, checked in by landauf, 17 years ago
added boost
File size: 269.4 KB

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1	// boost octonion.hpp header file
2
3	// (C) Copyright Hubert Holin 2001.
4	// Distributed under the Boost Software License, Version 1.0. (See
5	// accompanying file LICENSE_1_0.txt or copy at
6	// http://www.boost.org/LICENSE_1_0.txt)
7
8	// See http://www.boost.org for updates, documentation, and revision history.
9
10
11	#ifndef BOOST_OCTONION_HPP
12	#define BOOST_OCTONION_HPP
13
14	#include <boost/math/quaternion.hpp>
15
16
17	namespace boost
18	{
19	namespace math
20	{
21	#if BOOST_WORKAROUND(__GNUC__, < 3)
22	// gcc 2.95.x uses expression templates for valarray calculations, but
23	// the result is not conforming. We need BOOST_GET_VALARRAY to get an
24	// actual valarray result when we need to call a member function
25	#define BOOST_GET_VALARRAY(T,x) ::std::valarray<T>(x)
26	// gcc 2.95.x has an "std::ios" class that is similar to
27	// "std::ios_base", so we just use a #define
28	#define BOOST_IOS_BASE ::std::ios
29	// gcc 2.x ignores function scope using declarations,
30	// put them in the scope of the enclosing namespace instead:
31	using ::std::valarray;
32	using ::std::sqrt;
33	using ::std::cos;
34	using ::std::sin;
35	using ::std::exp;
36	using ::std::cosh;
37	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
38
39	#define BOOST_OCTONION_ACCESSOR_GENERATOR(type) \
40	type real() const \
41	{ \
42	return(a); \
43	} \
44	\
45	octonion<type> unreal() const \
46	{ \
47	return(octonion(static_cast<type>(0),b,c,d,e,f,g,h)); \
48	} \
49	\
50	type R_component_1() const \
51	{ \
52	return(a); \
53	} \
54	\
55	type R_component_2() const \
56	{ \
57	return(b); \
58	} \
59	\
60	type R_component_3() const \
61	{ \
62	return(c); \
63	} \
64	\
65	type R_component_4() const \
66	{ \
67	return(d); \
68	} \
69	\
70	type R_component_5() const \
71	{ \
72	return(e); \
73	} \
74	\
75	type R_component_6() const \
76	{ \
77	return(f); \
78	} \
79	\
80	type R_component_7() const \
81	{ \
82	return(g); \
83	} \
84	\
85	type R_component_8() const \
86	{ \
87	return(h); \
88	} \
89	\
90	::std::complex<type> C_component_1() const \
91	{ \
92	return(::std::complex<type>(a,b)); \
93	} \
94	\
95	::std::complex<type> C_component_2() const \
96	{ \
97	return(::std::complex<type>(c,d)); \
98	} \
99	\
100	::std::complex<type> C_component_3() const \
101	{ \
102	return(::std::complex<type>(e,f)); \
103	} \
104	\
105	::std::complex<type> C_component_4() const \
106	{ \
107	return(::std::complex<type>(g,h)); \
108	} \
109	\
110	::boost::math::quaternion<type> H_component_1() const \
111	{ \
112	return(::boost::math::quaternion<type>(a,b,c,d)); \
113	} \
114	\
115	::boost::math::quaternion<type> H_component_2() const \
116	{ \
117	return(::boost::math::quaternion<type>(e,f,g,h)); \
118	}
119
120
121	#define BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(type) \
122	template<typename X> \
123	octonion<type> & operator = (octonion<X> const & a_affecter) \
124	{ \
125	a = static_cast<type>(a_affecter.R_component_1()); \
126	b = static_cast<type>(a_affecter.R_component_2()); \
127	c = static_cast<type>(a_affecter.R_component_3()); \
128	d = static_cast<type>(a_affecter.R_component_4()); \
129	e = static_cast<type>(a_affecter.R_component_5()); \
130	f = static_cast<type>(a_affecter.R_component_6()); \
131	g = static_cast<type>(a_affecter.R_component_7()); \
132	h = static_cast<type>(a_affecter.R_component_8()); \
133	\
134	return(*this); \
135	} \
136	\
137	octonion<type> & operator = (octonion<type> const & a_affecter) \
138	{ \
139	a = a_affecter.a; \
140	b = a_affecter.b; \
141	c = a_affecter.c; \
142	d = a_affecter.d; \
143	e = a_affecter.e; \
144	f = a_affecter.f; \
145	g = a_affecter.g; \
146	h = a_affecter.h; \
147	\
148	return(*this); \
149	} \
150	\
151	octonion<type> & operator = (type const & a_affecter) \
152	{ \
153	a = a_affecter; \
154	\
155	b = c = d = e = f= g = h = static_cast<type>(0); \
156	\
157	return(*this); \
158	} \
159	\
160	octonion<type> & operator = (::std::complex<type> const & a_affecter) \
161	{ \
162	a = a_affecter.real(); \
163	b = a_affecter.imag(); \
164	\
165	c = d = e = f = g = h = static_cast<type>(0); \
166	\
167	return(*this); \
168	} \
169	\
170	octonion<type> & operator = (::boost::math::quaternion<type> const & a_affecter) \
171	{ \
172	a = a_affecter.R_component_1(); \
173	b = a_affecter.R_component_2(); \
174	c = a_affecter.R_component_3(); \
175	d = a_affecter.R_component_4(); \
176	\
177	e = f = g = h = static_cast<type>(0); \
178	\
179	return(*this); \
180	}
181
182
183	#define BOOST_OCTONION_MEMBER_DATA_GENERATOR(type) \
184	type a; \
185	type b; \
186	type c; \
187	type d; \
188	type e; \
189	type f; \
190	type g; \
191	type h; \
192
193
194	template<typename T>
195	class octonion
196	{
197	public:
198
199	typedef T value_type;
200
201	// constructor for O seen as R^8
202	// (also default constructor)
203
204	explicit octonion( T const & requested_a = T(),
205	T const & requested_b = T(),
206	T const & requested_c = T(),
207	T const & requested_d = T(),
208	T const & requested_e = T(),
209	T const & requested_f = T(),
210	T const & requested_g = T(),
211	T const & requested_h = T())
212	: a(requested_a),
213	b(requested_b),
214	c(requested_c),
215	d(requested_d),
216	e(requested_e),
217	f(requested_f),
218	g(requested_g),
219	h(requested_h)
220	{
221	// nothing to do!
222	}
223
224
225	// constructor for H seen as C^4
226
227	explicit octonion( ::std::complex<T> const & z0,
228	::std::complex<T> const & z1 = ::std::complex<T>(),
229	::std::complex<T> const & z2 = ::std::complex<T>(),
230	::std::complex<T> const & z3 = ::std::complex<T>())
231	: a(z0.real()),
232	b(z0.imag()),
233	c(z1.real()),
234	d(z1.imag()),
235	e(z2.real()),
236	f(z2.imag()),
237	g(z3.real()),
238	h(z3.imag())
239	{
240	// nothing to do!
241	}
242
243
244	// constructor for O seen as H^2
245
246	explicit octonion( ::boost::math::quaternion<T> const & q0,
247	::boost::math::quaternion<T> const & q1 = ::boost::math::quaternion<T>())
248	: a(q0.R_component_1()),
249	b(q0.R_component_2()),
250	c(q0.R_component_3()),
251	d(q0.R_component_4()),
252	e(q1.R_component_1()),
253	f(q1.R_component_2()),
254	g(q1.R_component_3()),
255	h(q1.R_component_4())
256	{
257	// nothing to do!
258	}
259
260
261	// UNtemplated copy constructor
262	// (this is taken care of by the compiler itself)
263
264
265	// templated copy constructor
266
267	template<typename X>
268	explicit octonion(octonion<X> const & a_recopier)
269	: a(static_cast<T>(a_recopier.R_component_1())),
270	b(static_cast<T>(a_recopier.R_component_2())),
271	c(static_cast<T>(a_recopier.R_component_3())),
272	d(static_cast<T>(a_recopier.R_component_4())),
273	e(static_cast<T>(a_recopier.R_component_5())),
274	f(static_cast<T>(a_recopier.R_component_6())),
275	g(static_cast<T>(a_recopier.R_component_7())),
276	h(static_cast<T>(a_recopier.R_component_8()))
277	{
278	// nothing to do!
279	}
280
281
282	// destructor
283	// (this is taken care of by the compiler itself)
284
285
286	// accessors
287	//
288	// Note: Like complex number, octonions do have a meaningful notion of "real part",
289	// but unlike them there is no meaningful notion of "imaginary part".
290	// Instead there is an "unreal part" which itself is an octonion, and usually
291	// nothing simpler (as opposed to the complex number case).
292	// However, for practicallity, there are accessors for the other components
293	// (these are necessary for the templated copy constructor, for instance).
294
295	BOOST_OCTONION_ACCESSOR_GENERATOR(T)
296
297	// assignment operators
298
299	BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(T)
300
301	// other assignment-related operators
302	//
303	// NOTE: Octonion multiplication is NOT commutative;
304	// symbolically, "q = rhs;" means "q = q rhs;"
305	// and "q /= rhs;" means "q = q * inverse_of(rhs);";
306	// octonion multiplication is also NOT associative
307
308	octonion<T> & operator += (T const & rhs)
309	{
310	T at = a + rhs; // exception guard
311
312	a = at;
313
314	return(*this);
315	}
316
317
318	octonion<T> & operator += (::std::complex<T> const & rhs)
319	{
320	T at = a + rhs.real(); // exception guard
321	T bt = b + rhs.imag(); // exception guard
322
323	a = at;
324	b = bt;
325
326	return(*this);
327	}
328
329
330	octonion<T> & operator += (::boost::math::quaternion<T> const & rhs)
331	{
332	T at = a + rhs.R_component_1(); // exception guard
333	T bt = b + rhs.R_component_2(); // exception guard
334	T ct = c + rhs.R_component_3(); // exception guard
335	T dt = d + rhs.R_component_4(); // exception guard
336
337	a = at;
338	b = bt;
339	c = ct;
340	d = dt;
341
342	return(*this);
343	}
344
345
346	template<typename X>
347	octonion<T> & operator += (octonion<X> const & rhs)
348	{
349	T at = a + static_cast<T>(rhs.R_component_1()); // exception guard
350	T bt = b + static_cast<T>(rhs.R_component_2()); // exception guard
351	T ct = c + static_cast<T>(rhs.R_component_3()); // exception guard
352	T dt = d + static_cast<T>(rhs.R_component_4()); // exception guard
353	T et = e + static_cast<T>(rhs.R_component_5()); // exception guard
354	T ft = f + static_cast<T>(rhs.R_component_6()); // exception guard
355	T gt = g + static_cast<T>(rhs.R_component_7()); // exception guard
356	T ht = h + static_cast<T>(rhs.R_component_8()); // exception guard
357
358	a = at;
359	b = bt;
360	c = ct;
361	d = dt;
362	e = et;
363	f = ft;
364	g = gt;
365	h = ht;
366
367	return(*this);
368	}
369
370
371
372	octonion<T> & operator -= (T const & rhs)
373	{
374	T at = a - rhs; // exception guard
375
376	a = at;
377
378	return(*this);
379	}
380
381
382	octonion<T> & operator -= (::std::complex<T> const & rhs)
383	{
384	T at = a - rhs.real(); // exception guard
385	T bt = b - rhs.imag(); // exception guard
386
387	a = at;
388	b = bt;
389
390	return(*this);
391	}
392
393
394	octonion<T> & operator -= (::boost::math::quaternion<T> const & rhs)
395	{
396	T at = a - rhs.R_component_1(); // exception guard
397	T bt = b - rhs.R_component_2(); // exception guard
398	T ct = c - rhs.R_component_3(); // exception guard
399	T dt = d - rhs.R_component_4(); // exception guard
400
401	a = at;
402	b = bt;
403	c = ct;
404	d = dt;
405
406	return(*this);
407	}
408
409
410	template<typename X>
411	octonion<T> & operator -= (octonion<X> const & rhs)
412	{
413	T at = a - static_cast<T>(rhs.R_component_1()); // exception guard
414	T bt = b - static_cast<T>(rhs.R_component_2()); // exception guard
415	T ct = c - static_cast<T>(rhs.R_component_3()); // exception guard
416	T dt = d - static_cast<T>(rhs.R_component_4()); // exception guard
417	T et = e - static_cast<T>(rhs.R_component_5()); // exception guard
418	T ft = f - static_cast<T>(rhs.R_component_6()); // exception guard
419	T gt = g - static_cast<T>(rhs.R_component_7()); // exception guard
420	T ht = h - static_cast<T>(rhs.R_component_8()); // exception guard
421
422	a = at;
423	b = bt;
424	c = ct;
425	d = dt;
426	e = et;
427	f = ft;
428	g = gt;
429	h = ht;
430
431	return(*this);
432	}
433
434
435	octonion<T> & operator *= (T const & rhs)
436	{
437	T at = a * rhs; // exception guard
438	T bt = b * rhs; // exception guard
439	T ct = c * rhs; // exception guard
440	T dt = d * rhs; // exception guard
441	T et = e * rhs; // exception guard
442	T ft = f * rhs; // exception guard
443	T gt = g * rhs; // exception guard
444	T ht = h * rhs; // exception guard
445
446	a = at;
447	b = bt;
448	c = ct;
449	d = dt;
450	e = et;
451	f = ft;
452	g = gt;
453	h = ht;
454
455	return(*this);
456	}
457
458
459	octonion<T> & operator *= (::std::complex<T> const & rhs)
460	{
461	T ar = rhs.real();
462	T br = rhs.imag();
463
464	T at = +aar-bbr;
465	T bt = +abr+bar;
466	T ct = +car+dbr;
467	T dt = -cbr+dar;
468	T et = +ear+fbr;
469	T ft = -ebr+far;
470	T gt = +gar-hbr;
471	T ht = +gbr+har;
472
473	a = at;
474	b = bt;
475	c = ct;
476	d = dt;
477	e = et;
478	f = ft;
479	g = gt;
480	h = ht;
481
482	return(*this);
483	}
484
485
486	octonion<T> & operator *= (::boost::math::quaternion<T> const & rhs)
487	{
488	T ar = rhs.R_component_1();
489	T br = rhs.R_component_2();
490	T cr = rhs.R_component_2();
491	T dr = rhs.R_component_2();
492
493	T at = +aar-bbr-ccr-ddr;
494	T bt = +abr+bar+cdr-dcr;
495	T ct = +acr-bdr+car+dbr;
496	T dt = +adr+bcr-cbr+dar;
497	T et = +ear+fbr+gcr+hdr;
498	T ft = -ebr+far-gdr+hcr;
499	T gt = -ecr+fdr+gar-hbr;
500	T ht = -edr-fcr+gbr+har;
501
502	a = at;
503	b = bt;
504	c = ct;
505	d = dt;
506	e = et;
507	f = ft;
508	g = gt;
509	h = ht;
510
511	return(*this);
512	}
513
514
515	template<typename X>
516	octonion<T> & operator *= (octonion<X> const & rhs)
517	{
518	T ar = static_cast<T>(rhs.R_component_1());
519	T br = static_cast<T>(rhs.R_component_2());
520	T cr = static_cast<T>(rhs.R_component_3());
521	T dr = static_cast<T>(rhs.R_component_4());
522	T er = static_cast<T>(rhs.R_component_5());
523	T fr = static_cast<T>(rhs.R_component_6());
524	T gr = static_cast<T>(rhs.R_component_7());
525	T hr = static_cast<T>(rhs.R_component_8());
526
527	T at = +aar-bbr-ccr-ddr-eer-ffr-ggr-hhr;
528	T bt = +abr+bar+cdr-dcr+efr-fer-ghr+hgr;
529	T ct = +acr-bdr+car+dbr+egr+fhr-ger-hfr;
530	T dt = +adr+bcr-cbr+dar+ehr-fgr+gfr-her;
531	T et = +aer-bfr-cgr-dhr+ear+fbr+gcr+hdr;
532	T ft = +afr+ber-chr+dgr-ebr+far-gdr+hcr;
533	T gt = +agr+bhr+cer-dfr-ecr+fdr+gar-hbr;
534	T ht = +ahr-bgr+cfr+der-edr-fcr+gbr+har;
535
536	a = at;
537	b = bt;
538	c = ct;
539	d = dt;
540	e = et;
541	f = ft;
542	g = gt;
543	h = ht;
544
545	return(*this);
546	}
547
548
549	octonion<T> & operator /= (T const & rhs)
550	{
551	T at = a / rhs; // exception guard
552	T bt = b / rhs; // exception guard
553	T ct = c / rhs; // exception guard
554	T dt = d / rhs; // exception guard
555	T et = e / rhs; // exception guard
556	T ft = f / rhs; // exception guard
557	T gt = g / rhs; // exception guard
558	T ht = h / rhs; // exception guard
559
560	a = at;
561	b = bt;
562	c = ct;
563	d = dt;
564	e = et;
565	f = ft;
566	g = gt;
567	h = ht;
568
569	return(*this);
570	}
571
572
573	octonion<T> & operator /= (::std::complex<T> const & rhs)
574	{
575	T ar = rhs.real();
576	T br = rhs.imag();
577
578	T denominator = arar+brbr;
579
580	T at = (+aar-bbr)/denominator;
581	T bt = (-abr+bar)/denominator;
582	T ct = (+car-dbr)/denominator;
583	T dt = (+cbr+dar)/denominator;
584	T et = (+ear-fbr)/denominator;
585	T ft = (+ebr+far)/denominator;
586	T gt = (+gar+hbr)/denominator;
587	T ht = (+gbr+har)/denominator;
588
589	a = at;
590	b = bt;
591	c = ct;
592	d = dt;
593	e = et;
594	f = ft;
595	g = gt;
596	h = ht;
597
598	return(*this);
599	}
600
601
602	octonion<T> & operator /= (::boost::math::quaternion<T> const & rhs)
603	{
604	T ar = rhs.R_component_1();
605	T br = rhs.R_component_2();
606	T cr = rhs.R_component_2();
607	T dr = rhs.R_component_2();
608
609	T denominator = arar+brbr+crcr+drdr;
610
611	T at = (+aar+bbr+ccr+ddr)/denominator;
612	T bt = (-abr+bar-cdr+dcr)/denominator;
613	T ct = (-acr+bdr+car-dbr)/denominator;
614	T dt = (-adr-bcr+cbr+dar)/denominator;
615	T et = (+ear-fbr-gcr-hdr)/denominator;
616	T ft = (+ebr+far+gdr-hcr)/denominator;
617	T gt = (+ecr-fdr+gar+hbr)/denominator;
618	T ht = (+edr+fcr-gbr+har)/denominator;
619
620	a = at;
621	b = bt;
622	c = ct;
623	d = dt;
624	e = et;
625	f = ft;
626	g = gt;
627	h = ht;
628
629	return(*this);
630	}
631
632
633	template<typename X>
634	octonion<T> & operator /= (octonion<X> const & rhs)
635	{
636	T ar = static_cast<T>(rhs.R_component_1());
637	T br = static_cast<T>(rhs.R_component_2());
638	T cr = static_cast<T>(rhs.R_component_3());
639	T dr = static_cast<T>(rhs.R_component_4());
640	T er = static_cast<T>(rhs.R_component_5());
641	T fr = static_cast<T>(rhs.R_component_6());
642	T gr = static_cast<T>(rhs.R_component_7());
643	T hr = static_cast<T>(rhs.R_component_8());
644
645	T denominator = arar+brbr+crcr+drdr+erer+frfr+grgr+hrhr;
646
647	T at = (+aar+bbr+ccr+ddr+eer+ffr+ggr+hhr)/denominator;
648	T bt = (-abr+bar-cdr+dcr-efr+fer+ghr-hgr)/denominator;
649	T ct = (-acr+bdr+car-dbr-egr-fhr+ger+hfr)/denominator;
650	T dt = (-adr-bcr+cbr+dar-ehr+fgr-gfr+her)/denominator;
651	T et = (-aer+bfr+cgr+dhr+ear-fbr-gcr-hdr)/denominator;
652	T ft = (-afr-ber+chr-dgr+ebr+far+gdr-hcr)/denominator;
653	T gt = (-agr-bhr-cer+dfr+ecr-fdr+gar+hbr)/denominator;
654	T ht = (-ahr+bgr-cfr-der+edr+fcr-gbr+har)/denominator;
655
656	a = at;
657	b = bt;
658	c = ct;
659	d = dt;
660	e = et;
661	f = ft;
662	g = gt;
663	h = ht;
664
665	return(*this);
666	}
667
668
669	protected:
670
671	BOOST_OCTONION_MEMBER_DATA_GENERATOR(T)
672
673
674	private:
675
676	};
677
678
679	// declaration of octonion specialization
680
681	template<> class octonion<float>;
682	template<> class octonion<double>;
683	template<> class octonion<long double>;
684
685
686	// helper templates for converting copy constructors (declaration)
687
688	namespace detail
689	{
690
691	template< typename T,
692	typename U
693	>
694	octonion<T> octonion_type_converter(octonion<U> const & rhs);
695	}
696
697
698	// implementation of octonion specialization
699
700
701	#define BOOST_OCTONION_CONSTRUCTOR_GENERATOR(type) \
702	explicit octonion( type const & requested_a = static_cast<type>(0), \
703	type const & requested_b = static_cast<type>(0), \
704	type const & requested_c = static_cast<type>(0), \
705	type const & requested_d = static_cast<type>(0), \
706	type const & requested_e = static_cast<type>(0), \
707	type const & requested_f = static_cast<type>(0), \
708	type const & requested_g = static_cast<type>(0), \
709	type const & requested_h = static_cast<type>(0)) \
710	: a(requested_a), \
711	b(requested_b), \
712	c(requested_c), \
713	d(requested_d), \
714	e(requested_e), \
715	f(requested_f), \
716	g(requested_g), \
717	h(requested_h) \
718	{ \
719	} \
720	\
721	explicit octonion( ::std::complex<type> const & z0, \
722	::std::complex<type> const & z1 = ::std::complex<type>(), \
723	::std::complex<type> const & z2 = ::std::complex<type>(), \
724	::std::complex<type> const & z3 = ::std::complex<type>()) \
725	: a(z0.real()), \
726	b(z0.imag()), \
727	c(z1.real()), \
728	d(z1.imag()), \
729	e(z2.real()), \
730	f(z2.imag()), \
731	g(z3.real()), \
732	h(z3.imag()) \
733	{ \
734	} \
735	\
736	explicit octonion( ::boost::math::quaternion<type> const & q0, \
737	::boost::math::quaternion<type> const & q1 = ::boost::math::quaternion<type>()) \
738	: a(q0.R_component_1()), \
739	b(q0.R_component_2()), \
740	c(q0.R_component_3()), \
741	d(q0.R_component_4()), \
742	e(q1.R_component_1()), \
743	f(q1.R_component_2()), \
744	g(q1.R_component_3()), \
745	h(q1.R_component_4()) \
746	{ \
747	}
748
749
750	#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_1(type) \
751	octonion<type> & operator += (type const & rhs) \
752	{ \
753	a += rhs; \
754	\
755	return(*this); \
756	}
757
758	#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_2(type) \
759	octonion<type> & operator += (::std::complex<type> const & rhs) \
760	{ \
761	a += rhs.real(); \
762	b += rhs.imag(); \
763	\
764	return(*this); \
765	}
766
767	#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_3(type) \
768	octonion<type> & operator += (::boost::math::quaternion<type> const & rhs) \
769	{ \
770	a += rhs.R_component_1(); \
771	b += rhs.R_component_2(); \
772	c += rhs.R_component_3(); \
773	d += rhs.R_component_4(); \
774	\
775	return(*this); \
776	}
777
778	#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_4(type) \
779	template<typename X> \
780	octonion<type> & operator += (octonion<X> const & rhs) \
781	{ \
782	a += static_cast<type>(rhs.R_component_1()); \
783	b += static_cast<type>(rhs.R_component_2()); \
784	c += static_cast<type>(rhs.R_component_3()); \
785	d += static_cast<type>(rhs.R_component_4()); \
786	e += static_cast<type>(rhs.R_component_5()); \
787	f += static_cast<type>(rhs.R_component_6()); \
788	g += static_cast<type>(rhs.R_component_7()); \
789	h += static_cast<type>(rhs.R_component_8()); \
790	\
791	return(*this); \
792	}
793
794	#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_1(type) \
795	octonion<type> & operator -= (type const & rhs) \
796	{ \
797	a -= rhs; \
798	\
799	return(*this); \
800	}
801
802	#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_2(type) \
803	octonion<type> & operator -= (::std::complex<type> const & rhs) \
804	{ \
805	a -= rhs.real(); \
806	b -= rhs.imag(); \
807	\
808	return(*this); \
809	}
810
811	#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_3(type) \
812	octonion<type> & operator -= (::boost::math::quaternion<type> const & rhs) \
813	{ \
814	a -= rhs.R_component_1(); \
815	b -= rhs.R_component_2(); \
816	c -= rhs.R_component_3(); \
817	d -= rhs.R_component_4(); \
818	\
819	return(*this); \
820	}
821
822	#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_4(type) \
823	template<typename X> \
824	octonion<type> & operator -= (octonion<X> const & rhs) \
825	{ \
826	a -= static_cast<type>(rhs.R_component_1()); \
827	b -= static_cast<type>(rhs.R_component_2()); \
828	c -= static_cast<type>(rhs.R_component_3()); \
829	d -= static_cast<type>(rhs.R_component_4()); \
830	e -= static_cast<type>(rhs.R_component_5()); \
831	f -= static_cast<type>(rhs.R_component_6()); \
832	g -= static_cast<type>(rhs.R_component_7()); \
833	h -= static_cast<type>(rhs.R_component_8()); \
834	\
835	return(*this); \
836	}
837
838	#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_1(type) \
839	octonion<type> & operator *= (type const & rhs) \
840	{ \
841	a *= rhs; \
842	b *= rhs; \
843	c *= rhs; \
844	d *= rhs; \
845	e *= rhs; \
846	f *= rhs; \
847	g *= rhs; \
848	h *= rhs; \
849	\
850	return(*this); \
851	}
852
853	#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_2(type) \
854	octonion<type> & operator *= (::std::complex<type> const & rhs) \
855	{ \
856	type ar = rhs.real(); \
857	type br = rhs.imag(); \
858	\
859	type at = +aar-bbr; \
860	type bt = +abr+bar; \
861	type ct = +car+dbr; \
862	type dt = -cbr+dar; \
863	type et = +ear+fbr; \
864	type ft = -ebr+far; \
865	type gt = +gar-hbr; \
866	type ht = +gbr+har; \
867	\
868	a = at; \
869	b = bt; \
870	c = ct; \
871	d = dt; \
872	e = et; \
873	f = ft; \
874	g = gt; \
875	h = ht; \
876	\
877	return(*this); \
878	}
879
880	#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type) \
881	octonion<type> & operator *= (::boost::math::quaternion<type> const & rhs) \
882	{ \
883	type ar = rhs.R_component_1(); \
884	type br = rhs.R_component_2(); \
885	type cr = rhs.R_component_2(); \
886	type dr = rhs.R_component_2(); \
887	\
888	type at = +aar-bbr-ccr-ddr; \
889	type bt = +abr+bar+cdr-dcr; \
890	type ct = +acr-bdr+car+dbr; \
891	type dt = +adr+bcr-cbr+dar; \
892	type et = +ear+fbr+gcr+hdr; \
893	type ft = -ebr+far-gdr+hcr; \
894	type gt = -ecr+fdr+gar-hbr; \
895	type ht = -edr-fcr+gbr+har; \
896	\
897	a = at; \
898	b = bt; \
899	c = ct; \
900	d = dt; \
901	e = et; \
902	f = ft; \
903	g = gt; \
904	h = ht; \
905	\
906	return(*this); \
907	}
908
909	#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type) \
910	template<typename X> \
911	octonion<type> & operator *= (octonion<X> const & rhs) \
912	{ \
913	type ar = static_cast<type>(rhs.R_component_1()); \
914	type br = static_cast<type>(rhs.R_component_2()); \
915	type cr = static_cast<type>(rhs.R_component_3()); \
916	type dr = static_cast<type>(rhs.R_component_4()); \
917	type er = static_cast<type>(rhs.R_component_5()); \
918	type fr = static_cast<type>(rhs.R_component_6()); \
919	type gr = static_cast<type>(rhs.R_component_7()); \
920	type hr = static_cast<type>(rhs.R_component_8()); \
921	\
922	type at = +aar-bbr-ccr-ddr-eer-ffr-ggr-hhr; \
923	type bt = +abr+bar+cdr-dcr+efr-fer-ghr+hgr; \
924	type ct = +acr-bdr+car+dbr+egr+fhr-ger-hfr; \
925	type dt = +adr+bcr-cbr+dar+ehr-fgr+gfr-her; \
926	type et = +aer-bfr-cgr-dhr+ear+fbr+gcr+hdr; \
927	type ft = +afr+ber-chr+dgr-ebr+far-gdr+hcr; \
928	type gt = +agr+bhr+cer-dfr-ecr+fdr+gar-hbr; \
929	type ht = +ahr-bgr+cfr+der-edr-fcr+gbr+har; \
930	\
931	a = at; \
932	b = bt; \
933	c = ct; \
934	d = dt; \
935	e = et; \
936	f = ft; \
937	g = gt; \
938	h = ht; \
939	\
940	return(*this); \
941	}
942
943	// There is quite a lot of repetition in the code below. This is intentional.
944	// The last conditional block is the normal form, and the others merely
945	// consist of workarounds for various compiler deficiencies. Hopefuly, when
946	// more compilers are conformant and we can retire support for those that are
947	// not, we will be able to remove the clutter. This is makes the situation
948	// (painfully) explicit.
949
950	#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type) \
951	octonion<type> & operator /= (type const & rhs) \
952	{ \
953	a /= rhs; \
954	b /= rhs; \
955	c /= rhs; \
956	d /= rhs; \
957	\
958	return(*this); \
959	}
960
961	#if defined(__GNUC__) && (__GNUC__ < 3)
962	#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
963	octonion<type> & operator /= (::std::complex<type> const & rhs) \
964	{ \
965	using ::std::valarray; \
966	\
967	valarray<type> tr(2); \
968	\
969	tr[0] = rhs.real(); \
970	tr[1] = rhs.imag(); \
971	\
972	type mixam = (BOOST_GET_VALARRAY(type,static_cast<type>(1)/abs(tr)).max)(); \
973	\
974	tr *= mixam; \
975	\
976	valarray<type> tt(8); \
977	\
978	tt[0] = +atr[0]-btr[1]; \
979	tt[1] = -atr[1]+btr[0]; \
980	tt[2] = +ctr[0]-dtr[1]; \
981	tt[3] = +ctr[1]+dtr[0]; \
982	tt[4] = +etr[0]-ftr[1]; \
983	tt[5] = +etr[1]+ftr[0]; \
984	tt[6] = +gtr[0]+htr[1]; \
985	tt[7] = +gtr[1]+htr[0]; \
986	\
987	tr *= tr; \
988	\
989	tt *= (mixam/tr.sum()); \
990	\
991	a = tt[0]; \
992	b = tt[1]; \
993	c = tt[2]; \
994	d = tt[3]; \
995	e = tt[4]; \
996	f = tt[5]; \
997	g = tt[6]; \
998	h = tt[7]; \
999	\
1000	return(*this); \
1001	}
1002	#elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
1003	#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
1004	octonion<type> & operator /= (::std::complex<type> const & rhs) \
1005	{ \
1006	using ::std::valarray; \
1007	using ::std::abs; \
1008	\
1009	valarray<type> tr(2); \
1010	\
1011	tr[0] = rhs.real(); \
1012	tr[1] = rhs.imag(); \
1013	\
1014	type mixam = static_cast<type>(1)/(abs(tr).max)(); \
1015	\
1016	tr *= mixam; \
1017	\
1018	valarray<type> tt(8); \
1019	\
1020	tt[0] = +atr[0]-btr[1]; \
1021	tt[1] = -atr[1]+btr[0]; \
1022	tt[2] = +ctr[0]-dtr[1]; \
1023	tt[3] = +ctr[1]+dtr[0]; \
1024	tt[4] = +etr[0]-ftr[1]; \
1025	tt[5] = +etr[1]+ftr[0]; \
1026	tt[6] = +gtr[0]+htr[1]; \
1027	tt[7] = +gtr[1]+htr[0]; \
1028	\
1029	tr *= tr; \
1030	\
1031	tt *= (mixam/tr.sum()); \
1032	\
1033	a = tt[0]; \
1034	b = tt[1]; \
1035	c = tt[2]; \
1036	d = tt[3]; \
1037	e = tt[4]; \
1038	f = tt[5]; \
1039	g = tt[6]; \
1040	h = tt[7]; \
1041	\
1042	return(*this); \
1043	}
1044	#else
1045	#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
1046	octonion<type> & operator /= (::std::complex<type> const & rhs) \
1047	{ \
1048	using ::std::valarray; \
1049	\
1050	valarray<type> tr(2); \
1051	\
1052	tr[0] = rhs.real(); \
1053	tr[1] = rhs.imag(); \
1054	\
1055	type mixam = static_cast<type>(1)/(abs(tr).max)(); \
1056	\
1057	tr *= mixam; \
1058	\
1059	valarray<type> tt(8); \
1060	\
1061	tt[0] = +atr[0]-btr[1]; \
1062	tt[1] = -atr[1]+btr[0]; \
1063	tt[2] = +ctr[0]-dtr[1]; \
1064	tt[3] = +ctr[1]+dtr[0]; \
1065	tt[4] = +etr[0]-ftr[1]; \
1066	tt[5] = +etr[1]+ftr[0]; \
1067	tt[6] = +gtr[0]+htr[1]; \
1068	tt[7] = +gtr[1]+htr[0]; \
1069	\
1070	tr *= tr; \
1071	\
1072	tt *= (mixam/tr.sum()); \
1073	\
1074	a = tt[0]; \
1075	b = tt[1]; \
1076	c = tt[2]; \
1077	d = tt[3]; \
1078	e = tt[4]; \
1079	f = tt[5]; \
1080	g = tt[6]; \
1081	h = tt[7]; \
1082	\
1083	return(*this); \
1084	}
1085	#endif /* defined(__GNUC__) && (__GNUC__ < 3) / / BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
1086
1087	#if defined(__GNUC__) && (__GNUC__ < 3)
1088	#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
1089	octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \
1090	{ \
1091	using ::std::valarray; \
1092	\
1093	valarray<type> tr(4); \
1094	\
1095	tr[0] = static_cast<type>(rhs.R_component_1()); \
1096	tr[1] = static_cast<type>(rhs.R_component_2()); \
1097	tr[2] = static_cast<type>(rhs.R_component_3()); \
1098	tr[3] = static_cast<type>(rhs.R_component_4()); \
1099	\
1100	type mixam = (BOOST_GET_VALARRAY(type,static_cast<type>(1)/abs(tr)).max)();\
1101	\
1102	tr *= mixam; \
1103	\
1104	valarray<type> tt(8); \
1105	\
1106	tt[0] = +atr[0]+btr[1]+ctr[2]+dtr[3]; \
1107	tt[1] = -atr[1]+btr[0]-ctr[3]+dtr[2]; \
1108	tt[2] = -atr[2]+btr[3]+ctr[0]-dtr[1]; \
1109	tt[3] = -atr[3]-btr[2]+ctr[1]+dtr[0]; \
1110	tt[4] = +etr[0]-ftr[1]-gtr[2]-htr[3]; \
1111	tt[5] = +etr[1]+ftr[0]+gtr[3]-htr[2]; \
1112	tt[6] = +etr[2]-ftr[3]+gtr[0]+htr[1]; \
1113	tt[7] = +etr[3]+ftr[2]-gtr[1]+htr[0]; \
1114	\
1115	tr *= tr; \
1116	\
1117	tt *= (mixam/tr.sum()); \
1118	\
1119	a = tt[0]; \
1120	b = tt[1]; \
1121	c = tt[2]; \
1122	d = tt[3]; \
1123	e = tt[4]; \
1124	f = tt[5]; \
1125	g = tt[6]; \
1126	h = tt[7]; \
1127	\
1128	return(*this); \
1129	}
1130	#elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
1131	#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
1132	octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \
1133	{ \
1134	using ::std::valarray; \
1135	using ::std::abs; \
1136	\
1137	valarray<type> tr(4); \
1138	\
1139	tr[0] = static_cast<type>(rhs.R_component_1()); \
1140	tr[1] = static_cast<type>(rhs.R_component_2()); \
1141	tr[2] = static_cast<type>(rhs.R_component_3()); \
1142	tr[3] = static_cast<type>(rhs.R_component_4()); \
1143	\
1144	type mixam = static_cast<type>(1)/(abs(tr).max)(); \
1145	\
1146	tr *= mixam; \
1147	\
1148	valarray<type> tt(8); \
1149	\
1150	tt[0] = +atr[0]+btr[1]+ctr[2]+dtr[3]; \
1151	tt[1] = -atr[1]+btr[0]-ctr[3]+dtr[2]; \
1152	tt[2] = -atr[2]+btr[3]+ctr[0]-dtr[1]; \
1153	tt[3] = -atr[3]-btr[2]+ctr[1]+dtr[0]; \
1154	tt[4] = +etr[0]-ftr[1]-gtr[2]-htr[3]; \
1155	tt[5] = +etr[1]+ftr[0]+gtr[3]-htr[2]; \
1156	tt[6] = +etr[2]-ftr[3]+gtr[0]+htr[1]; \
1157	tt[7] = +etr[3]+ftr[2]-gtr[1]+htr[0]; \
1158	\
1159	tr *= tr; \
1160	\
1161	tt *= (mixam/tr.sum()); \
1162	\
1163	a = tt[0]; \
1164	b = tt[1]; \
1165	c = tt[2]; \
1166	d = tt[3]; \
1167	e = tt[4]; \
1168	f = tt[5]; \
1169	g = tt[6]; \
1170	h = tt[7]; \
1171	\
1172	return(*this); \
1173	}
1174	#else
1175	#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
1176	octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \
1177	{ \
1178	using ::std::valarray; \
1179	\
1180	valarray<type> tr(4); \
1181	\
1182	tr[0] = static_cast<type>(rhs.R_component_1()); \
1183	tr[1] = static_cast<type>(rhs.R_component_2()); \
1184	tr[2] = static_cast<type>(rhs.R_component_3()); \
1185	tr[3] = static_cast<type>(rhs.R_component_4()); \
1186	\
1187	type mixam = static_cast<type>(1)/(abs(tr).max)(); \
1188	\
1189	tr *= mixam; \
1190	\
1191	valarray<type> tt(8); \
1192	\
1193	tt[0] = +atr[0]+btr[1]+ctr[2]+dtr[3]; \
1194	tt[1] = -atr[1]+btr[0]-ctr[3]+dtr[2]; \
1195	tt[2] = -atr[2]+btr[3]+ctr[0]-dtr[1]; \
1196	tt[3] = -atr[3]-btr[2]+ctr[1]+dtr[0]; \
1197	tt[4] = +etr[0]-ftr[1]-gtr[2]-htr[3]; \
1198	tt[5] = +etr[1]+ftr[0]+gtr[3]-htr[2]; \
1199	tt[6] = +etr[2]-ftr[3]+gtr[0]+htr[1]; \
1200	tt[7] = +etr[3]+ftr[2]-gtr[1]+htr[0]; \
1201	\
1202	tr *= tr; \
1203	\
1204	tt *= (mixam/tr.sum()); \
1205	\
1206	a = tt[0]; \
1207	b = tt[1]; \
1208	c = tt[2]; \
1209	d = tt[3]; \
1210	e = tt[4]; \
1211	f = tt[5]; \
1212	g = tt[6]; \
1213	h = tt[7]; \
1214	\
1215	return(*this); \
1216	}
1217	#endif /* defined(__GNUC__) && (__GNUC__ < 3) / / BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
1218
1219	#if defined(__GNUC__) && (__GNUC__ < 3)
1220	#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
1221	template<typename X> \
1222	octonion<type> & operator /= (octonion<X> const & rhs) \
1223	{ \
1224	using ::std::valarray; \
1225	\
1226	valarray<type> tr(8); \
1227	\
1228	tr[0] = static_cast<type>(rhs.R_component_1()); \
1229	tr[1] = static_cast<type>(rhs.R_component_2()); \
1230	tr[2] = static_cast<type>(rhs.R_component_3()); \
1231	tr[3] = static_cast<type>(rhs.R_component_4()); \
1232	tr[4] = static_cast<type>(rhs.R_component_5()); \
1233	tr[5] = static_cast<type>(rhs.R_component_6()); \
1234	tr[6] = static_cast<type>(rhs.R_component_7()); \
1235	tr[7] = static_cast<type>(rhs.R_component_8()); \
1236	\
1237	type mixam = (BOOST_GET_VALARRAY(type,static_cast<type>(1)/abs(tr)).max)();\
1238	\
1239	tr *= mixam; \
1240	\
1241	valarray<type> tt(8); \
1242	\
1243	tt[0] = +atr[0]+btr[1]+ctr[2]+dtr[3]+etr[4]+ftr[5]+gtr[6]+htr[7]; \
1244	tt[1] = -atr[1]+btr[0]-ctr[3]+dtr[2]-etr[5]+ftr[4]+gtr[7]-htr[6]; \
1245	tt[2] = -atr[2]+btr[3]+ctr[0]-dtr[1]-etr[6]-ftr[7]+gtr[4]+htr[5]; \
1246	tt[3] = -atr[3]-btr[2]+ctr[1]+dtr[0]-etr[7]+ftr[6]-gtr[5]+htr[4]; \
1247	tt[4] = -atr[4]+btr[5]+ctr[6]+dtr[7]+etr[0]-ftr[1]-gtr[2]-htr[3]; \
1248	tt[5] = -atr[5]-btr[4]+ctr[7]-dtr[6]+etr[1]+ftr[0]+gtr[3]-htr[2]; \
1249	tt[6] = -atr[6]-btr[7]-ctr[4]+dtr[5]+etr[2]-ftr[3]+gtr[0]+htr[1]; \
1250	tt[7] = -atr[7]+btr[6]-ctr[5]-dtr[4]+etr[3]+ftr[2]-gtr[1]+htr[0]; \
1251	\
1252	tr *= tr; \
1253	\
1254	tt *= (mixam/tr.sum()); \
1255	\
1256	a = tt[0]; \
1257	b = tt[1]; \
1258	c = tt[2]; \
1259	d = tt[3]; \
1260	e = tt[4]; \
1261	f = tt[5]; \
1262	g = tt[6]; \
1263	h = tt[7]; \
1264	\
1265	return(*this); \
1266	}
1267	#elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
1268	#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
1269	template<typename X> \
1270	octonion<type> & operator /= (octonion<X> const & rhs) \
1271	{ \
1272	using ::std::valarray; \
1273	using ::std::abs; \
1274	\
1275	valarray<type> tr(8); \
1276	\
1277	tr[0] = static_cast<type>(rhs.R_component_1()); \
1278	tr[1] = static_cast<type>(rhs.R_component_2()); \
1279	tr[2] = static_cast<type>(rhs.R_component_3()); \
1280	tr[3] = static_cast<type>(rhs.R_component_4()); \
1281	tr[4] = static_cast<type>(rhs.R_component_5()); \
1282	tr[5] = static_cast<type>(rhs.R_component_6()); \
1283	tr[6] = static_cast<type>(rhs.R_component_7()); \
1284	tr[7] = static_cast<type>(rhs.R_component_8()); \
1285	\
1286	type mixam = static_cast<type>(1)/(abs(tr).max)(); \
1287	\
1288	tr *= mixam; \
1289	\
1290	valarray<type> tt(8); \
1291	\
1292	tt[0] = +atr[0]+btr[1]+ctr[2]+dtr[3]+etr[4]+ftr[5]+gtr[6]+htr[7]; \
1293	tt[1] = -atr[1]+btr[0]-ctr[3]+dtr[2]-etr[5]+ftr[4]+gtr[7]-htr[6]; \
1294	tt[2] = -atr[2]+btr[3]+ctr[0]-dtr[1]-etr[6]-ftr[7]+gtr[4]+htr[5]; \
1295	tt[3] = -atr[3]-btr[2]+ctr[1]+dtr[0]-etr[7]+ftr[6]-gtr[5]+htr[4]; \
1296	tt[4] = -atr[4]+btr[5]+ctr[6]+dtr[7]+etr[0]-ftr[1]-gtr[2]-htr[3]; \
1297	tt[5] = -atr[5]-btr[4]+ctr[7]-dtr[6]+etr[1]+ftr[0]+gtr[3]-htr[2]; \
1298	tt[6] = -atr[6]-btr[7]-ctr[4]+dtr[5]+etr[2]-ftr[3]+gtr[0]+htr[1]; \
1299	tt[7] = -atr[7]+btr[6]-ctr[5]-dtr[4]+etr[3]+ftr[2]-gtr[1]+htr[0]; \
1300	\
1301	tr *= tr; \
1302	\
1303	tt *= (mixam/tr.sum()); \
1304	\
1305	a = tt[0]; \
1306	b = tt[1]; \
1307	c = tt[2]; \
1308	d = tt[3]; \
1309	e = tt[4]; \
1310	f = tt[5]; \
1311	g = tt[6]; \
1312	h = tt[7]; \
1313	\
1314	return(*this); \
1315	}
1316	#else
1317	#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
1318	template<typename X> \
1319	octonion<type> & operator /= (octonion<X> const & rhs) \
1320	{ \
1321	using ::std::valarray; \
1322	\
1323	valarray<type> tr(8); \
1324	\
1325	tr[0] = static_cast<type>(rhs.R_component_1()); \
1326	tr[1] = static_cast<type>(rhs.R_component_2()); \
1327	tr[2] = static_cast<type>(rhs.R_component_3()); \
1328	tr[3] = static_cast<type>(rhs.R_component_4()); \
1329	tr[4] = static_cast<type>(rhs.R_component_5()); \
1330	tr[5] = static_cast<type>(rhs.R_component_6()); \
1331	tr[6] = static_cast<type>(rhs.R_component_7()); \
1332	tr[7] = static_cast<type>(rhs.R_component_8()); \
1333	\
1334	type mixam = static_cast<type>(1)/(abs(tr).max)(); \
1335	\
1336	tr *= mixam; \
1337	\
1338	valarray<type> tt(8); \
1339	\
1340	tt[0] = +atr[0]+btr[1]+ctr[2]+dtr[3]+etr[4]+ftr[5]+gtr[6]+htr[7]; \
1341	tt[1] = -atr[1]+btr[0]-ctr[3]+dtr[2]-etr[5]+ftr[4]+gtr[7]-htr[6]; \
1342	tt[2] = -atr[2]+btr[3]+ctr[0]-dtr[1]-etr[6]-ftr[7]+gtr[4]+htr[5]; \
1343	tt[3] = -atr[3]-btr[2]+ctr[1]+dtr[0]-etr[7]+ftr[6]-gtr[5]+htr[4]; \
1344	tt[4] = -atr[4]+btr[5]+ctr[6]+dtr[7]+etr[0]-ftr[1]-gtr[2]-htr[3]; \
1345	tt[5] = -atr[5]-btr[4]+ctr[7]-dtr[6]+etr[1]+ftr[0]+gtr[3]-htr[2]; \
1346	tt[6] = -atr[6]-btr[7]-ctr[4]+dtr[5]+etr[2]-ftr[3]+gtr[0]+htr[1]; \
1347	tt[7] = -atr[7]+btr[6]-ctr[5]-dtr[4]+etr[3]+ftr[2]-gtr[1]+htr[0]; \
1348	\
1349	tr *= tr; \
1350	\
1351	tt *= (mixam/tr.sum()); \
1352	\
1353	a = tt[0]; \
1354	b = tt[1]; \
1355	c = tt[2]; \
1356	d = tt[3]; \
1357	e = tt[4]; \
1358	f = tt[5]; \
1359	g = tt[6]; \
1360	h = tt[7]; \
1361	\
1362	return(*this); \
1363	}
1364	#endif /* defined(__GNUC__) && (__GNUC__ < 3) / / BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
1365
1366
1367	#define BOOST_OCTONION_MEMBER_ADD_GENERATOR(type) \
1368	BOOST_OCTONION_MEMBER_ADD_GENERATOR_1(type) \
1369	BOOST_OCTONION_MEMBER_ADD_GENERATOR_2(type) \
1370	BOOST_OCTONION_MEMBER_ADD_GENERATOR_3(type) \
1371	BOOST_OCTONION_MEMBER_ADD_GENERATOR_4(type)
1372
1373	#define BOOST_OCTONION_MEMBER_SUB_GENERATOR(type) \
1374	BOOST_OCTONION_MEMBER_SUB_GENERATOR_1(type) \
1375	BOOST_OCTONION_MEMBER_SUB_GENERATOR_2(type) \
1376	BOOST_OCTONION_MEMBER_SUB_GENERATOR_3(type) \
1377	BOOST_OCTONION_MEMBER_SUB_GENERATOR_4(type)
1378
1379	#define BOOST_OCTONION_MEMBER_MUL_GENERATOR(type) \
1380	BOOST_OCTONION_MEMBER_MUL_GENERATOR_1(type) \
1381	BOOST_OCTONION_MEMBER_MUL_GENERATOR_2(type) \
1382	BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type) \
1383	BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type)
1384
1385	#define BOOST_OCTONION_MEMBER_DIV_GENERATOR(type) \
1386	BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type) \
1387	BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
1388	BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
1389	BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type)
1390
1391	#define BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(type) \
1392	BOOST_OCTONION_MEMBER_ADD_GENERATOR(type) \
1393	BOOST_OCTONION_MEMBER_SUB_GENERATOR(type) \
1394	BOOST_OCTONION_MEMBER_MUL_GENERATOR(type) \
1395	BOOST_OCTONION_MEMBER_DIV_GENERATOR(type)
1396
1397
1398	template<>
1399	class octonion<float>
1400	{
1401	public:
1402
1403	typedef float value_type;
1404
1405	BOOST_OCTONION_CONSTRUCTOR_GENERATOR(float)
1406
1407	// UNtemplated copy constructor
1408	// (this is taken care of by the compiler itself)
1409
1410	// explicit copy constructors (precision-loosing converters)
1411
1412	explicit octonion(octonion<double> const & a_recopier)
1413	{
1414	*this = detail::octonion_type_converter<float, double>(a_recopier);
1415	}
1416
1417	explicit octonion(octonion<long double> const & a_recopier)
1418	{
1419	*this = detail::octonion_type_converter<float, long double>(a_recopier);
1420	}
1421
1422	// destructor
1423	// (this is taken care of by the compiler itself)
1424
1425	// accessors
1426	//
1427	// Note: Like complex number, octonions do have a meaningful notion of "real part",
1428	// but unlike them there is no meaningful notion of "imaginary part".
1429	// Instead there is an "unreal part" which itself is an octonion, and usually
1430	// nothing simpler (as opposed to the complex number case).
1431	// However, for practicallity, there are accessors for the other components
1432	// (these are necessary for the templated copy constructor, for instance).
1433
1434	BOOST_OCTONION_ACCESSOR_GENERATOR(float)
1435
1436	// assignment operators
1437
1438	BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(float)
1439
1440	// other assignment-related operators
1441	//
1442	// NOTE: Octonion multiplication is NOT commutative;
1443	// symbolically, "q = rhs;" means "q = q rhs;"
1444	// and "q /= rhs;" means "q = q * inverse_of(rhs);";
1445	// octonion multiplication is also NOT associative
1446
1447	BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(float)
1448
1449
1450	protected:
1451
1452	BOOST_OCTONION_MEMBER_DATA_GENERATOR(float)
1453
1454
1455	private:
1456
1457	};
1458
1459
1460	template<>
1461	class octonion<double>
1462	{
1463	public:
1464
1465	typedef double value_type;
1466
1467	BOOST_OCTONION_CONSTRUCTOR_GENERATOR(double)
1468
1469	// UNtemplated copy constructor
1470	// (this is taken care of by the compiler itself)
1471
1472	// converting copy constructor
1473
1474	explicit octonion(octonion<float> const & a_recopier)
1475	{
1476	*this = detail::octonion_type_converter<double, float>(a_recopier);
1477	}
1478
1479	// explicit copy constructors (precision-loosing converters)
1480
1481	explicit octonion(octonion<long double> const & a_recopier)
1482	{
1483	*this = detail::octonion_type_converter<double, long double>(a_recopier);
1484	}
1485
1486	// destructor
1487	// (this is taken care of by the compiler itself)
1488
1489	// accessors
1490	//
1491	// Note: Like complex number, octonions do have a meaningful notion of "real part",
1492	// but unlike them there is no meaningful notion of "imaginary part".
1493	// Instead there is an "unreal part" which itself is an octonion, and usually
1494	// nothing simpler (as opposed to the complex number case).
1495	// However, for practicallity, there are accessors for the other components
1496	// (these are necessary for the templated copy constructor, for instance).
1497
1498	BOOST_OCTONION_ACCESSOR_GENERATOR(double)
1499
1500	// assignment operators
1501
1502	BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(double)
1503
1504	// other assignment-related operators
1505	//
1506	// NOTE: Octonion multiplication is NOT commutative;
1507	// symbolically, "q = rhs;" means "q = q rhs;"
1508	// and "q /= rhs;" means "q = q * inverse_of(rhs);";
1509	// octonion multiplication is also NOT associative
1510
1511	BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(double)
1512
1513
1514	protected:
1515
1516	BOOST_OCTONION_MEMBER_DATA_GENERATOR(double)
1517
1518
1519	private:
1520
1521	};
1522
1523
1524	template<>
1525	class octonion<long double>
1526	{
1527	public:
1528
1529	typedef long double value_type;
1530
1531	BOOST_OCTONION_CONSTRUCTOR_GENERATOR(long double)
1532
1533	// UNtemplated copy constructor
1534	// (this is taken care of by the compiler itself)
1535
1536	// converting copy constructor
1537
1538	explicit octonion(octonion<float> const & a_recopier)
1539	{
1540	*this = detail::octonion_type_converter<long double, float>(a_recopier);
1541	}
1542
1543
1544	explicit octonion(octonion<double> const & a_recopier)
1545	{
1546	*this = detail::octonion_type_converter<long double, double>(a_recopier);
1547	}
1548
1549
1550	// destructor
1551	// (this is taken care of by the compiler itself)
1552
1553	// accessors
1554	//
1555	// Note: Like complex number, octonions do have a meaningful notion of "real part",
1556	// but unlike them there is no meaningful notion of "imaginary part".
1557	// Instead there is an "unreal part" which itself is an octonion, and usually
1558	// nothing simpler (as opposed to the complex number case).
1559	// However, for practicallity, there are accessors for the other components
1560	// (these are necessary for the templated copy constructor, for instance).
1561
1562	BOOST_OCTONION_ACCESSOR_GENERATOR(long double)
1563
1564	// assignment operators
1565
1566	BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(long double)
1567
1568	// other assignment-related operators
1569	//
1570	// NOTE: Octonion multiplication is NOT commutative;
1571	// symbolically, "q = rhs;" means "q = q rhs;"
1572	// and "q /= rhs;" means "q = q * inverse_of(rhs);";
1573	// octonion multiplication is also NOT associative
1574
1575	BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(long double)
1576
1577
1578	protected:
1579
1580	BOOST_OCTONION_MEMBER_DATA_GENERATOR(long double)
1581
1582
1583	private:
1584
1585	};
1586
1587
1588	#undef BOOST_OCTONION_CONSTRUCTOR_GENERATOR
1589
1590	#undef BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR
1591
1592	#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR
1593	#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR
1594	#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR
1595	#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR
1596
1597	#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_1
1598	#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_2
1599	#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_3
1600	#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_4
1601	#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_1
1602	#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_2
1603	#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_3
1604	#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_4
1605	#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_1
1606	#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_2
1607	#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_3
1608	#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_4
1609	#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_1
1610	#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_2
1611	#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_3
1612	#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_4
1613
1614
1615	#undef BOOST_OCTONION_MEMBER_DATA_GENERATOR
1616
1617	#undef BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR
1618
1619	#undef BOOST_OCTONION_ACCESSOR_GENERATOR
1620
1621
1622	// operators
1623
1624	#define BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) \
1625	{ \
1626	octonion<T> res(lhs); \
1627	res op##= rhs; \
1628	return(res); \
1629	}
1630
1631	#define BOOST_OCTONION_OPERATOR_GENERATOR_1_L(op) \
1632	template<typename T> \
1633	inline octonion<T> operator op (T const & lhs, octonion<T> const & rhs) \
1634	BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1635
1636	#define BOOST_OCTONION_OPERATOR_GENERATOR_1_R(op) \
1637	template<typename T> \
1638	inline octonion<T> operator op (octonion<T> const & lhs, T const & rhs) \
1639	BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1640
1641	#define BOOST_OCTONION_OPERATOR_GENERATOR_2_L(op) \
1642	template<typename T> \
1643	inline octonion<T> operator op (::std::complex<T> const & lhs, octonion<T> const & rhs) \
1644	BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1645
1646	#define BOOST_OCTONION_OPERATOR_GENERATOR_2_R(op) \
1647	template<typename T> \
1648	inline octonion<T> operator op (octonion<T> const & lhs, ::std::complex<T> const & rhs) \
1649	BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1650
1651	#define BOOST_OCTONION_OPERATOR_GENERATOR_3_L(op) \
1652	template<typename T> \
1653	inline octonion<T> operator op (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs) \
1654	BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1655
1656	#define BOOST_OCTONION_OPERATOR_GENERATOR_3_R(op) \
1657	template<typename T> \
1658	inline octonion<T> operator op (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs) \
1659	BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1660
1661	#define BOOST_OCTONION_OPERATOR_GENERATOR_4(op) \
1662	template<typename T> \
1663	inline octonion<T> operator op (octonion<T> const & lhs, octonion<T> const & rhs) \
1664	BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1665
1666	#define BOOST_OCTONION_OPERATOR_GENERATOR(op) \
1667	BOOST_OCTONION_OPERATOR_GENERATOR_1_L(op) \
1668	BOOST_OCTONION_OPERATOR_GENERATOR_1_R(op) \
1669	BOOST_OCTONION_OPERATOR_GENERATOR_2_L(op) \
1670	BOOST_OCTONION_OPERATOR_GENERATOR_2_R(op) \
1671	BOOST_OCTONION_OPERATOR_GENERATOR_3_L(op) \
1672	BOOST_OCTONION_OPERATOR_GENERATOR_3_R(op) \
1673	BOOST_OCTONION_OPERATOR_GENERATOR_4(op)
1674
1675
1676	BOOST_OCTONION_OPERATOR_GENERATOR(+)
1677	BOOST_OCTONION_OPERATOR_GENERATOR(-)
1678	BOOST_OCTONION_OPERATOR_GENERATOR(*)
1679	BOOST_OCTONION_OPERATOR_GENERATOR(/)
1680
1681
1682	#undef BOOST_OCTONION_OPERATOR_GENERATOR
1683
1684	#undef BOOST_OCTONION_OPERATOR_GENERATOR_1_L
1685	#undef BOOST_OCTONION_OPERATOR_GENERATOR_1_R
1686	#undef BOOST_OCTONION_OPERATOR_GENERATOR_2_L
1687	#undef BOOST_OCTONION_OPERATOR_GENERATOR_2_R
1688	#undef BOOST_OCTONION_OPERATOR_GENERATOR_3_L
1689	#undef BOOST_OCTONION_OPERATOR_GENERATOR_3_R
1690	#undef BOOST_OCTONION_OPERATOR_GENERATOR_4
1691
1692	#undef BOOST_OCTONION_OPERATOR_GENERATOR_BODY
1693
1694
1695	template<typename T>
1696	inline octonion<T> operator + (octonion<T> const & o)
1697	{
1698	return(o);
1699	}
1700
1701
1702	template<typename T>
1703	inline octonion<T> operator - (octonion<T> const & o)
1704	{
1705	return(octonion<T>(-o.R_component_1(),-o.R_component_2(),-o.R_component_3(),-o.R_component_4(),-o.R_component_5(),-o.R_component_6(),-o.R_component_7(),-o.R_component_8()));
1706	}
1707
1708
1709	template<typename T>
1710	inline bool operator == (T const & lhs, octonion<T> const & rhs)
1711	{
1712	return(
1713	(rhs.R_component_1() == lhs)&&
1714	(rhs.R_component_2() == static_cast<T>(0))&&
1715	(rhs.R_component_3() == static_cast<T>(0))&&
1716	(rhs.R_component_4() == static_cast<T>(0))&&
1717	(rhs.R_component_5() == static_cast<T>(0))&&
1718	(rhs.R_component_6() == static_cast<T>(0))&&
1719	(rhs.R_component_7() == static_cast<T>(0))&&
1720	(rhs.R_component_8() == static_cast<T>(0))
1721	);
1722	}
1723
1724
1725	template<typename T>
1726	inline bool operator == (octonion<T> const & lhs, T const & rhs)
1727	{
1728	return(
1729	(lhs.R_component_1() == rhs)&&
1730	(lhs.R_component_2() == static_cast<T>(0))&&
1731	(lhs.R_component_3() == static_cast<T>(0))&&
1732	(lhs.R_component_4() == static_cast<T>(0))&&
1733	(lhs.R_component_5() == static_cast<T>(0))&&
1734	(lhs.R_component_6() == static_cast<T>(0))&&
1735	(lhs.R_component_7() == static_cast<T>(0))&&
1736	(lhs.R_component_8() == static_cast<T>(0))
1737	);
1738	}
1739
1740
1741	template<typename T>
1742	inline bool operator == (::std::complex<T> const & lhs, octonion<T> const & rhs)
1743	{
1744	return(
1745	(rhs.R_component_1() == lhs.real())&&
1746	(rhs.R_component_2() == lhs.imag())&&
1747	(rhs.R_component_3() == static_cast<T>(0))&&
1748	(rhs.R_component_4() == static_cast<T>(0))&&
1749	(rhs.R_component_5() == static_cast<T>(0))&&
1750	(rhs.R_component_6() == static_cast<T>(0))&&
1751	(rhs.R_component_7() == static_cast<T>(0))&&
1752	(rhs.R_component_8() == static_cast<T>(0))
1753	);
1754	}
1755
1756
1757	template<typename T>
1758	inline bool operator == (octonion<T> const & lhs, ::std::complex<T> const & rhs)
1759	{
1760	return(
1761	(lhs.R_component_1() == rhs.real())&&
1762	(lhs.R_component_2() == rhs.imag())&&
1763	(lhs.R_component_3() == static_cast<T>(0))&&
1764	(lhs.R_component_4() == static_cast<T>(0))&&
1765	(lhs.R_component_5() == static_cast<T>(0))&&
1766	(lhs.R_component_6() == static_cast<T>(0))&&
1767	(lhs.R_component_7() == static_cast<T>(0))&&
1768	(lhs.R_component_8() == static_cast<T>(0))
1769	);
1770	}
1771
1772
1773	template<typename T>
1774	inline bool operator == (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs)
1775	{
1776	return(
1777	(rhs.R_component_1() == lhs.R_component_1())&&
1778	(rhs.R_component_2() == lhs.R_component_2())&&
1779	(rhs.R_component_3() == lhs.R_component_3())&&
1780	(rhs.R_component_4() == lhs.R_component_4())&&
1781	(rhs.R_component_5() == static_cast<T>(0))&&
1782	(rhs.R_component_6() == static_cast<T>(0))&&
1783	(rhs.R_component_7() == static_cast<T>(0))&&
1784	(rhs.R_component_8() == static_cast<T>(0))
1785	);
1786	}
1787
1788
1789	template<typename T>
1790	inline bool operator == (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs)
1791	{
1792	return(
1793	(lhs.R_component_1() == rhs.R_component_1())&&
1794	(lhs.R_component_2() == rhs.R_component_2())&&
1795	(lhs.R_component_3() == rhs.R_component_3())&&
1796	(lhs.R_component_4() == rhs.R_component_4())&&
1797	(lhs.R_component_5() == static_cast<T>(0))&&
1798	(lhs.R_component_6() == static_cast<T>(0))&&
1799	(lhs.R_component_7() == static_cast<T>(0))&&
1800	(lhs.R_component_8() == static_cast<T>(0))
1801	);
1802	}
1803
1804
1805	template<typename T>
1806	inline bool operator == (octonion<T> const & lhs, octonion<T> const & rhs)
1807	{
1808	return(
1809	(rhs.R_component_1() == lhs.R_component_1())&&
1810	(rhs.R_component_2() == lhs.R_component_2())&&
1811	(rhs.R_component_3() == lhs.R_component_3())&&
1812	(rhs.R_component_4() == lhs.R_component_4())&&
1813	(rhs.R_component_5() == lhs.R_component_5())&&
1814	(rhs.R_component_6() == lhs.R_component_6())&&
1815	(rhs.R_component_7() == lhs.R_component_7())&&
1816	(rhs.R_component_8() == lhs.R_component_8())
1817	);
1818	}
1819
1820
1821	#define BOOST_OCTONION_NOT_EQUAL_GENERATOR \
1822	{ \
1823	return(!(lhs == rhs)); \
1824	}
1825
1826	template<typename T>
1827	inline bool operator != (T const & lhs, octonion<T> const & rhs)
1828	BOOST_OCTONION_NOT_EQUAL_GENERATOR
1829
1830	template<typename T>
1831	inline bool operator != (octonion<T> const & lhs, T const & rhs)
1832	BOOST_OCTONION_NOT_EQUAL_GENERATOR
1833
1834	template<typename T>
1835	inline bool operator != (::std::complex<T> const & lhs, octonion<T> const & rhs)
1836	BOOST_OCTONION_NOT_EQUAL_GENERATOR
1837
1838	template<typename T>
1839	inline bool operator != (octonion<T> const & lhs, ::std::complex<T> const & rhs)
1840	BOOST_OCTONION_NOT_EQUAL_GENERATOR
1841
1842	template<typename T>
1843	inline bool operator != (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs)
1844	BOOST_OCTONION_NOT_EQUAL_GENERATOR
1845
1846	template<typename T>
1847	inline bool operator != (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs)
1848	BOOST_OCTONION_NOT_EQUAL_GENERATOR
1849
1850	template<typename T>
1851	inline bool operator != (octonion<T> const & lhs, octonion<T> const & rhs)
1852	BOOST_OCTONION_NOT_EQUAL_GENERATOR
1853
1854	#undef BOOST_OCTONION_NOT_EQUAL_GENERATOR
1855
1856
1857	// Note: the default values in the constructors of the complex and quaternions make for
1858	// a very complex and ambiguous situation; we have made choices to disambiguate.
1859
1860	#if BOOST_WORKAROUND(__GNUC__, < 3)
1861	template<typename T>
1862	::std::istream & operator >> ( ::std::istream & is,
1863	octonion<T>& o)
1864	#else
1865	template<typename T, typename charT, class traits>
1866	::std::basic_istream<charT,traits> & operator >> ( ::std::basic_istream<charT,traits> & is,
1867	octonion<T> & o)
1868	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1869	{
1870	#if BOOST_WORKAROUND(__GNUC__, < 3)
1871	typedef char charT;
1872	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1873
1874	#ifdef BOOST_NO_STD_LOCALE
1875	#else
1876	const ::std::ctype<charT> & ct = ::std::use_facet< ::std::ctype<charT> >(is.getloc());
1877	#endif /* BOOST_NO_STD_LOCALE */
1878
1879	T a = T();
1880	T b = T();
1881	T c = T();
1882	T d = T();
1883	T e = T();
1884	T f = T();
1885	T g = T();
1886	T h = T();
1887
1888	::std::complex<T> u = ::std::complex<T>();
1889	::std::complex<T> v = ::std::complex<T>();
1890	::std::complex<T> x = ::std::complex<T>();
1891	::std::complex<T> y = ::std::complex<T>();
1892
1893	::boost::math::quaternion<T> p = ::boost::math::quaternion<T>();
1894	::boost::math::quaternion<T> q = ::boost::math::quaternion<T>();
1895
1896	charT ch = charT();
1897	char cc;
1898
1899	is >> ch; // get the first lexeme
1900
1901	if (!is.good()) goto finish;
1902
1903	#ifdef BOOST_NO_STD_LOCALE
1904	cc = ch;
1905	#else
1906	cc = ct.narrow(ch, char());
1907	#endif /* BOOST_NO_STD_LOCALE */
1908
1909	if (cc == '(') // read "("
1910	{
1911	is >> ch; // get the second lexeme
1912
1913	if (!is.good()) goto finish;
1914
1915	#ifdef BOOST_NO_STD_LOCALE
1916	cc = ch;
1917	#else
1918	cc = ct.narrow(ch, char());
1919	#endif /* BOOST_NO_STD_LOCALE */
1920
1921	if (cc == '(') // read "(("
1922	{
1923	is >> ch; // get the third lexeme
1924
1925	if (!is.good()) goto finish;
1926
1927	#ifdef BOOST_NO_STD_LOCALE
1928	cc = ch;
1929	#else
1930	cc = ct.narrow(ch, char());
1931	#endif /* BOOST_NO_STD_LOCALE */
1932
1933	if (cc == '(') // read "((("
1934	{
1935	is.putback(ch);
1936
1937	is >> u; // read "((u"
1938
1939	if (!is.good()) goto finish;
1940
1941	is >> ch; // get the next lexeme
1942
1943	if (!is.good()) goto finish;
1944
1945	#ifdef BOOST_NO_STD_LOCALE
1946	cc = ch;
1947	#else
1948	cc = ct.narrow(ch, char());
1949	#endif /* BOOST_NO_STD_LOCALE */
1950
1951	if (cc == ')') // read "((u)"
1952	{
1953	is >> ch; // get the next lexeme
1954
1955	if (!is.good()) goto finish;
1956
1957	#ifdef BOOST_NO_STD_LOCALE
1958	cc = ch;
1959	#else
1960	cc = ct.narrow(ch, char());
1961	#endif /* BOOST_NO_STD_LOCALE */
1962
1963	if (cc == ')') // format: (((a))), (((a,b)))
1964	{
1965	o = octonion<T>(u);
1966	}
1967	else if (cc == ',') // read "((u),"
1968	{
1969	p = ::boost::math::quaternion<T>(u);
1970
1971	is >> q; // read "((u),q"
1972
1973	if (!is.good()) goto finish;
1974
1975	is >> ch; // get the next lexeme
1976
1977	if (!is.good()) goto finish;
1978
1979	#ifdef BOOST_NO_STD_LOCALE
1980	cc = ch;
1981	#else
1982	cc = ct.narrow(ch, char());
1983	#endif /* BOOST_NO_STD_LOCALE */
1984
1985	if (cc == ')') // format: (((a)),q), (((a,b)),q)
1986	{
1987	o = octonion<T>(p,q);
1988	}
1989	else // error
1990	{
1991	#if BOOST_WORKAROUND(__GNUC__, < 3)
1992	is.setstate(::std::ios::failbit);
1993	#else
1994	is.setstate(::std::ios_base::failbit);
1995	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1996	}
1997	}
1998	else // error
1999	{
2000	#if BOOST_WORKAROUND(__GNUC__, < 3)
2001	is.setstate(::std::ios::failbit);
2002	#else
2003	is.setstate(::std::ios_base::failbit);
2004	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2005	}
2006	}
2007	else if (cc ==',') // read "((u,"
2008	{
2009	is >> v; // read "((u,v"
2010
2011	if (!is.good()) goto finish;
2012
2013	is >> ch; // get the next lexeme
2014
2015	if (!is.good()) goto finish;
2016
2017	#ifdef BOOST_NO_STD_LOCALE
2018	cc = ch;
2019	#else
2020	cc = ct.narrow(ch, char());
2021	#endif /* BOOST_NO_STD_LOCALE */
2022
2023	if (cc == ')') // read "((u,v)"
2024	{
2025	p = ::boost::math::quaternion<T>(u,v);
2026
2027	is >> ch; // get the next lexeme
2028
2029	if (!is.good()) goto finish;
2030
2031	#ifdef BOOST_NO_STD_LOCALE
2032	cc = ch;
2033	#else
2034	cc = ct.narrow(ch, char());
2035	#endif /* BOOST_NO_STD_LOCALE */
2036
2037	if (cc == ')') // format: (((a),v)), (((a,b),v))
2038	{
2039	o = octonion<T>(p);
2040	}
2041	else if (cc == ',') // read "((u,v),"
2042	{
2043	is >> q; // read "(p,q"
2044
2045	if (!is.good()) goto finish;
2046
2047	is >> ch; // get the next lexeme
2048
2049	if (!is.good()) goto finish;
2050
2051	#ifdef BOOST_NO_STD_LOCALE
2052	cc = ch;
2053	#else
2054	cc = ct.narrow(ch, char());
2055	#endif /* BOOST_NO_STD_LOCALE */
2056
2057	if (cc == ')') // format: (((a),v),q), (((a,b),v),q)
2058	{
2059	o = octonion<T>(p,q);
2060	}
2061	else // error
2062	{
2063	#if BOOST_WORKAROUND(__GNUC__, < 3)
2064	is.setstate(::std::ios::failbit);
2065	#else
2066	is.setstate(::std::ios_base::failbit);
2067	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2068	}
2069	}
2070	else // error
2071	{
2072	#if BOOST_WORKAROUND(__GNUC__, < 3)
2073	is.setstate(::std::ios::failbit);
2074	#else
2075	is.setstate(::std::ios_base::failbit);
2076	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2077	}
2078	}
2079	else // error
2080	{
2081	#if BOOST_WORKAROUND(__GNUC__, < 3)
2082	is.setstate(::std::ios::failbit);
2083	#else
2084	is.setstate(::std::ios_base::failbit);
2085	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2086	}
2087	}
2088	else // error
2089	{
2090	#if BOOST_WORKAROUND(__GNUC__, < 3)
2091	is.setstate(::std::ios::failbit);
2092	#else
2093	is.setstate(::std::ios_base::failbit);
2094	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2095	}
2096	}
2097	else // read "((a"
2098	{
2099	is.putback(ch);
2100
2101	is >> a; // we extract the first component
2102
2103	if (!is.good()) goto finish;
2104
2105	is >> ch; // get the next lexeme
2106
2107	if (!is.good()) goto finish;
2108
2109	#ifdef BOOST_NO_STD_LOCALE
2110	cc = ch;
2111	#else
2112	cc = ct.narrow(ch, char());
2113	#endif /* BOOST_NO_STD_LOCALE */
2114
2115	if (cc == ')') // read "((a)"
2116	{
2117	is >> ch; // get the next lexeme
2118
2119	if (!is.good()) goto finish;
2120
2121	#ifdef BOOST_NO_STD_LOCALE
2122	cc = ch;
2123	#else
2124	cc = ct.narrow(ch, char());
2125	#endif /* BOOST_NO_STD_LOCALE */
2126
2127	if (cc == ')') // read "((a))"
2128	{
2129	o = octonion<T>(a);
2130	}
2131	else if (cc == ',') // read "((a),"
2132	{
2133	is >> ch; // get the next lexeme
2134
2135	if (!is.good()) goto finish;
2136
2137	#ifdef BOOST_NO_STD_LOCALE
2138	cc = ch;
2139	#else
2140	cc = ct.narrow(ch, char());
2141	#endif /* BOOST_NO_STD_LOCALE */
2142
2143	if (cc == '(') // read "((a),("
2144	{
2145	is >> ch; // get the next lexeme
2146
2147	if (!is.good()) goto finish;
2148
2149	#ifdef BOOST_NO_STD_LOCALE
2150	cc = ch;
2151	#else
2152	cc = ct.narrow(ch, char());
2153	#endif /* BOOST_NO_STD_LOCALE */
2154
2155	if (cc == '(') // read "((a),(("
2156	{
2157	is.putback(ch);
2158
2159	is.putback(ch); // we backtrack twice, with the same value!
2160
2161	is >> q; // read "((a),q"
2162
2163	if (!is.good()) goto finish;
2164
2165	is >> ch; // get the next lexeme
2166
2167	if (!is.good()) goto finish;
2168
2169	#ifdef BOOST_NO_STD_LOCALE
2170	cc = ch;
2171	#else
2172	cc = ct.narrow(ch, char());
2173	#endif /* BOOST_NO_STD_LOCALE */
2174
2175	if (cc == ')') // read "((a),q)"
2176	{
2177	p = ::boost::math::quaternion<T>(a);
2178
2179	o = octonion<T>(p,q);
2180	}
2181	else // error
2182	{
2183	#if BOOST_WORKAROUND(__GNUC__, < 3)
2184	is.setstate(::std::ios::failbit);
2185	#else
2186	is.setstate(::std::ios_base::failbit);
2187	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2188	}
2189	}
2190	else // read "((a),(c" or "((a),(e"
2191	{
2192	is.putback(ch);
2193
2194	is >> c;
2195
2196	if (!is.good()) goto finish;
2197
2198	is >> ch; // get the next lexeme
2199
2200	if (!is.good()) goto finish;
2201
2202	#ifdef BOOST_NO_STD_LOCALE
2203	cc = ch;
2204	#else
2205	cc = ct.narrow(ch, char());
2206	#endif /* BOOST_NO_STD_LOCALE */
2207
2208	if (cc == ')') // read "((a),(c)" (ambiguity resolution)
2209	{
2210	is >> ch; // get the next lexeme
2211
2212	if (!is.good()) goto finish;
2213
2214	#ifdef BOOST_NO_STD_LOCALE
2215	cc = ch;
2216	#else
2217	cc = ct.narrow(ch, char());
2218	#endif /* BOOST_NO_STD_LOCALE */
2219
2220	if (cc == ')') // read "((a),(c))"
2221	{
2222	o = octonion<T>(a,b,c);
2223	}
2224	else if (cc == ',') // read "((a),(c),"
2225	{
2226	u = ::std::complex<T>(a);
2227
2228	v = ::std::complex<T>(c);
2229
2230	is >> x; // read "((a),(c),x"
2231
2232	if (!is.good()) goto finish;
2233
2234	is >> ch; // get the next lexeme
2235
2236	if (!is.good()) goto finish;
2237
2238	#ifdef BOOST_NO_STD_LOCALE
2239	cc = ch;
2240	#else
2241	cc = ct.narrow(ch, char());
2242	#endif /* BOOST_NO_STD_LOCALE */
2243
2244	if (cc == ')') // read "((a),(c),x)"
2245	{
2246	o = octonion<T>(u,v,x);
2247	}
2248	else if (cc == ',') // read "((a),(c),x,"
2249	{
2250	is >> y; // read "((a),(c),x,y"
2251
2252	if (!is.good()) goto finish;
2253
2254	is >> ch; // get the next lexeme
2255
2256	if (!is.good()) goto finish;
2257
2258	#ifdef BOOST_NO_STD_LOCALE
2259	cc = ch;
2260	#else
2261	cc = ct.narrow(ch, char());
2262	#endif /* BOOST_NO_STD_LOCALE */
2263
2264	if (cc == ')') // read "((a),(c),x,y)"
2265	{
2266	o = octonion<T>(u,v,x,y);
2267	}
2268	else // error
2269	{
2270	#if BOOST_WORKAROUND(__GNUC__, < 3)
2271	is.setstate(::std::ios::failbit);
2272	#else
2273	is.setstate(::std::ios_base::failbit);
2274	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2275	}
2276	}
2277	else // error
2278	{
2279	#if BOOST_WORKAROUND(__GNUC__, < 3)
2280	is.setstate(::std::ios::failbit);
2281	#else
2282	is.setstate(::std::ios_base::failbit);
2283	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2284	}
2285	}
2286	else // error
2287	{
2288	#if BOOST_WORKAROUND(__GNUC__, < 3)
2289	is.setstate(::std::ios::failbit);
2290	#else
2291	is.setstate(::std::ios_base::failbit);
2292	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2293	}
2294	}
2295	else if (cc == ',') // read "((a),(c," or "((a),(e,"
2296	{
2297	is >> ch; // get the next lexeme
2298
2299	if (!is.good()) goto finish;
2300
2301	#ifdef BOOST_NO_STD_LOCALE
2302	cc = ch;
2303	#else
2304	cc = ct.narrow(ch, char());
2305	#endif /* BOOST_NO_STD_LOCALE */
2306
2307	if (cc == '(') // read "((a),(e,(" (ambiguity resolution)
2308	{
2309	p = ::boost::math::quaternion<T>(a);
2310
2311	x = ::std::complex<T>(c); // "c" was actually "e"
2312
2313	is.putback(ch); // we can only backtrace once
2314
2315	is >> y; // read "((a),(e,y"
2316
2317	if (!is.good()) goto finish;
2318
2319	is >> ch; // get the next lexeme
2320
2321	#ifdef BOOST_NO_STD_LOCALE
2322	cc = ch;
2323	#else
2324	cc = ct.narrow(ch, char());
2325	#endif /* BOOST_NO_STD_LOCALE */
2326
2327	if (cc == ')') // read "((a),(e,y)"
2328	{
2329	q = ::boost::math::quaternion<T>(x,y);
2330
2331	is >> ch; // get the next lexeme
2332
2333	#ifdef BOOST_NO_STD_LOCALE
2334	cc = ch;
2335	#else
2336	cc = ct.narrow(ch, char());
2337	#endif /* BOOST_NO_STD_LOCALE */
2338
2339	if (cc == ')') // read "((a),(e,y))"
2340	{
2341	o = octonion<T>(p,q);
2342	}
2343	else // error
2344	{
2345	#if BOOST_WORKAROUND(__GNUC__, < 3)
2346	is.setstate(::std::ios::failbit);
2347	#else
2348	is.setstate(::std::ios_base::failbit);
2349	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2350	}
2351	}
2352	else // error
2353	{
2354	#if BOOST_WORKAROUND(__GNUC__, < 3)
2355	is.setstate(::std::ios::failbit);
2356	#else
2357	is.setstate(::std::ios_base::failbit);
2358	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2359	}
2360	}
2361	else // read "((a),(c,d" or "((a),(e,f"
2362	{
2363	is.putback(ch);
2364
2365	is >> d;
2366
2367	if (!is.good()) goto finish;
2368
2369	is >> ch; // get the next lexeme
2370
2371	if (!is.good()) goto finish;
2372
2373	#ifdef BOOST_NO_STD_LOCALE
2374	cc = ch;
2375	#else
2376	cc = ct.narrow(ch, char());
2377	#endif /* BOOST_NO_STD_LOCALE */
2378
2379	if (cc == ')') // read "((a),(c,d)" (ambiguity resolution)
2380	{
2381	is >> ch; // get the next lexeme
2382
2383	if (!is.good()) goto finish;
2384
2385	#ifdef BOOST_NO_STD_LOCALE
2386	cc = ch;
2387	#else
2388	cc = ct.narrow(ch, char());
2389	#endif /* BOOST_NO_STD_LOCALE */
2390
2391	if (cc == ')') // read "((a),(c,d))"
2392	{
2393	o = octonion<T>(a,b,c,d);
2394	}
2395	else if (cc == ',') // read "((a),(c,d),"
2396	{
2397	u = ::std::complex<T>(a);
2398
2399	v = ::std::complex<T>(c,d);
2400
2401	is >> x; // read "((a),(c,d),x"
2402
2403	if (!is.good()) goto finish;
2404
2405	is >> ch; // get the next lexeme
2406
2407	if (!is.good()) goto finish;
2408
2409	#ifdef BOOST_NO_STD_LOCALE
2410	cc = ch;
2411	#else
2412	cc = ct.narrow(ch, char());
2413	#endif /* BOOST_NO_STD_LOCALE */
2414
2415	if (cc == ')') // read "((a),(c,d),x)"
2416	{
2417	o = octonion<T>(u,v,x);
2418	}
2419	else if (cc == ',') // read "((a),(c,d),x,"
2420	{
2421	is >> y; // read "((a),(c,d),x,y"
2422
2423	if (!is.good()) goto finish;
2424
2425	is >> ch; // get the next lexeme
2426
2427	if (!is.good()) goto finish;
2428
2429	#ifdef BOOST_NO_STD_LOCALE
2430	cc = ch;
2431	#else
2432	cc = ct.narrow(ch, char());
2433	#endif /* BOOST_NO_STD_LOCALE */
2434
2435	if (cc == ')') // read "((a),(c,d),x,y)"
2436	{
2437	o = octonion<T>(u,v,x,y);
2438	}
2439	else // error
2440	{
2441	#if BOOST_WORKAROUND(__GNUC__, < 3)
2442	is.setstate(::std::ios::failbit);
2443	#else
2444	is.setstate(::std::ios_base::failbit);
2445	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2446	}
2447	}
2448	else // error
2449	{
2450	#if BOOST_WORKAROUND(__GNUC__, < 3)
2451	is.setstate(::std::ios::failbit);
2452	#else
2453	is.setstate(::std::ios_base::failbit);
2454	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2455	}
2456	}
2457	else // error
2458	{
2459	#if BOOST_WORKAROUND(__GNUC__, < 3)
2460	is.setstate(::std::ios::failbit);
2461	#else
2462	is.setstate(::std::ios_base::failbit);
2463	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2464	}
2465	}
2466	else if (cc == ',') // read "((a),(e,f," (ambiguity resolution)
2467	{
2468	p = ::boost::math::quaternion<T>(a);
2469
2470	is >> g; // read "((a),(e,f,g" (too late to backtrack)
2471
2472	if (!is.good()) goto finish;
2473
2474	is >> ch; // get the next lexeme
2475
2476	if (!is.good()) goto finish;
2477
2478	#ifdef BOOST_NO_STD_LOCALE
2479	cc = ch;
2480	#else
2481	cc = ct.narrow(ch, char());
2482	#endif /* BOOST_NO_STD_LOCALE */
2483
2484	if (cc == ')') // read "((a),(e,f,g)"
2485	{
2486	q = ::boost::math::quaternion<T>(c,d,g); // "c" was actually "e", and "d" was actually "f"
2487
2488	is >> ch; // get the next lexeme
2489
2490	if (!is.good()) goto finish;
2491
2492	#ifdef BOOST_NO_STD_LOCALE
2493	cc = ch;
2494	#else
2495	cc = ct.narrow(ch, char());
2496	#endif /* BOOST_NO_STD_LOCALE */
2497
2498	if (cc == ')') // read "((a),(e,f,g))"
2499	{
2500	o = octonion<T>(p,q);
2501	}
2502	else // error
2503	{
2504	#if BOOST_WORKAROUND(__GNUC__, < 3)
2505	is.setstate(::std::ios::failbit);
2506	#else
2507	is.setstate(::std::ios_base::failbit);
2508	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2509	}
2510	}
2511	else if (cc == ',') // read "((a),(e,f,g,"
2512	{
2513	is >> h; // read "((a),(e,f,g,h"
2514
2515	if (!is.good()) goto finish;
2516
2517	is >> ch; // get the next lexeme
2518
2519	if (!is.good()) goto finish;
2520
2521	#ifdef BOOST_NO_STD_LOCALE
2522	cc = ch;
2523	#else
2524	cc = ct.narrow(ch, char());
2525	#endif /* BOOST_NO_STD_LOCALE */
2526
2527	if (cc == ')') // read "((a),(e,f,g,h)"
2528	{
2529	q = ::boost::math::quaternion<T>(c,d,g,h); // "c" was actually "e", and "d" was actually "f"
2530
2531	is >> ch; // get the next lexeme
2532
2533	if (!is.good()) goto finish;
2534
2535	#ifdef BOOST_NO_STD_LOCALE
2536	cc = ch;
2537	#else
2538	cc = ct.narrow(ch, char());
2539	#endif /* BOOST_NO_STD_LOCALE */
2540
2541	if (cc == ')') // read "((a),(e,f,g,h))"
2542	{
2543	o = octonion<T>(p,q);
2544	}
2545	else // error
2546	{
2547	#if BOOST_WORKAROUND(__GNUC__, < 3)
2548	is.setstate(::std::ios::failbit);
2549	#else
2550	is.setstate(::std::ios_base::failbit);
2551	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2552	}
2553	}
2554	else // error
2555	{
2556	#if BOOST_WORKAROUND(__GNUC__, < 3)
2557	is.setstate(::std::ios::failbit);
2558	#else
2559	is.setstate(::std::ios_base::failbit);
2560	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2561	}
2562	}
2563	else // error
2564	{
2565	#if BOOST_WORKAROUND(__GNUC__, < 3)
2566	is.setstate(::std::ios::failbit);
2567	#else
2568	is.setstate(::std::ios_base::failbit);
2569	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2570	}
2571	}
2572	else // error
2573	{
2574	#if BOOST_WORKAROUND(__GNUC__, < 3)
2575	is.setstate(::std::ios::failbit);
2576	#else
2577	is.setstate(::std::ios_base::failbit);
2578	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2579	}
2580	}
2581	}
2582	else // error
2583	{
2584	#if BOOST_WORKAROUND(__GNUC__, < 3)
2585	is.setstate(::std::ios::failbit);
2586	#else
2587	is.setstate(::std::ios_base::failbit);
2588	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2589	}
2590	}
2591	}
2592	else // read "((a),c" (ambiguity resolution)
2593	{
2594	is.putback(ch);
2595
2596	is >> c; // we extract the third component
2597
2598	if (!is.good()) goto finish;
2599
2600	is >> ch; // get the next lexeme
2601
2602	if (!is.good()) goto finish;
2603
2604	#ifdef BOOST_NO_STD_LOCALE
2605	cc = ch;
2606	#else
2607	cc = ct.narrow(ch, char());
2608	#endif /* BOOST_NO_STD_LOCALE */
2609
2610	if (cc == ')') // read "((a),c)"
2611	{
2612	o = octonion<T>(a,b,c);
2613	}
2614	else if (cc == ',') // read "((a),c,"
2615	{
2616	is >> x; // read "((a),c,x"
2617
2618	if (!is.good()) goto finish;
2619
2620	is >> ch; // get the next lexeme
2621
2622	if (!is.good()) goto finish;
2623
2624	#ifdef BOOST_NO_STD_LOCALE
2625	cc = ch;
2626	#else
2627	cc = ct.narrow(ch, char());
2628	#endif /* BOOST_NO_STD_LOCALE */
2629
2630	if (cc == ')') // read "((a),c,x)"
2631	{
2632	o = octonion<T>(a,b,c,d,x.real(),x.imag());
2633	}
2634	else if (cc == ',') // read "((a),c,x,"
2635	{
2636	is >> y;if (!is.good()) goto finish; // read "((a),c,x,y"
2637
2638	is >> ch; // get the next lexeme
2639
2640	if (!is.good()) goto finish;
2641
2642	#ifdef BOOST_NO_STD_LOCALE
2643	cc = ch;
2644	#else
2645	cc = ct.narrow(ch, char());
2646	#endif /* BOOST_NO_STD_LOCALE */
2647
2648	if (cc == ')') // read "((a),c,x,y)"
2649	{
2650	o = octonion<T>(a,b,c,d,x.real(),x.imag(),y.real(),y.imag());
2651	}
2652	else // error
2653	{
2654	#if BOOST_WORKAROUND(__GNUC__, < 3)
2655	is.setstate(::std::ios::failbit);
2656	#else
2657	is.setstate(::std::ios_base::failbit);
2658	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2659	}
2660	}
2661	else // error
2662	{
2663	#if BOOST_WORKAROUND(__GNUC__, < 3)
2664	is.setstate(::std::ios::failbit);
2665	#else
2666	is.setstate(::std::ios_base::failbit);
2667	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2668	}
2669	}
2670	else // error
2671	{
2672	#if BOOST_WORKAROUND(__GNUC__, < 3)
2673	is.setstate(::std::ios::failbit);
2674	#else
2675	is.setstate(::std::ios_base::failbit);
2676	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2677	}
2678	}
2679	}
2680	else // error
2681	{
2682	#if BOOST_WORKAROUND(__GNUC__, < 3)
2683	is.setstate(::std::ios::failbit);
2684	#else
2685	is.setstate(::std::ios_base::failbit);
2686	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2687	}
2688	}
2689	else if (cc ==',') // read "((a,"
2690	{
2691	is >> ch; // get the next lexeme
2692
2693	if (!is.good()) goto finish;
2694
2695	#ifdef BOOST_NO_STD_LOCALE
2696	cc = ch;
2697	#else
2698	cc = ct.narrow(ch, char());
2699	#endif /* BOOST_NO_STD_LOCALE */
2700
2701	if (cc == '(') // read "((a,("
2702	{
2703	u = ::std::complex<T>(a);
2704
2705	is.putback(ch); // can only backtrack so much
2706
2707	is >> v; // read "((a,v"
2708
2709	if (!is.good()) goto finish;
2710
2711	is >> ch; // get the next lexeme
2712
2713	if (!is.good()) goto finish;
2714
2715	#ifdef BOOST_NO_STD_LOCALE
2716	cc = ch;
2717	#else
2718	cc = ct.narrow(ch, char());
2719	#endif /* BOOST_NO_STD_LOCALE */
2720
2721	if (cc == ')') // read "((a,v)"
2722	{
2723	is >> ch; // get the next lexeme
2724
2725	if (!is.good()) goto finish;
2726
2727	#ifdef BOOST_NO_STD_LOCALE
2728	cc = ch;
2729	#else
2730	cc = ct.narrow(ch, char());
2731	#endif /* BOOST_NO_STD_LOCALE */
2732
2733	if (cc == ')') // read "((a,v))"
2734	{
2735	o = octonion<T>(u,v);
2736	}
2737	else if (cc == ',') // read "((a,v),"
2738	{
2739	p = ::boost::math::quaternion<T>(u,v);
2740
2741	is >> q; // read "((a,v),q"
2742
2743	if (!is.good()) goto finish;
2744
2745	is >> ch; // get the next lexeme
2746
2747	if (!is.good()) goto finish;
2748
2749	#ifdef BOOST_NO_STD_LOCALE
2750	cc = ch;
2751	#else
2752	cc = ct.narrow(ch, char());
2753	#endif /* BOOST_NO_STD_LOCALE */
2754
2755	if (cc == ')') // read "((a,v),q)"
2756	{
2757	o = octonion<T>(p,q);
2758	}
2759	else // error
2760	{
2761	#if BOOST_WORKAROUND(__GNUC__, < 3)
2762	is.setstate(::std::ios::failbit);
2763	#else
2764	is.setstate(::std::ios_base::failbit);
2765	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2766	}
2767	}
2768	else // error
2769	{
2770	#if BOOST_WORKAROUND(__GNUC__, < 3)
2771	is.setstate(::std::ios::failbit);
2772	#else
2773	is.setstate(::std::ios_base::failbit);
2774	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2775	}
2776	}
2777	else // error
2778	{
2779	#if BOOST_WORKAROUND(__GNUC__, < 3)
2780	is.setstate(::std::ios::failbit);
2781	#else
2782	is.setstate(::std::ios_base::failbit);
2783	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2784	}
2785	}
2786	else
2787	{
2788	is.putback(ch);
2789
2790	is >> b; // read "((a,b"
2791
2792	if (!is.good()) goto finish;
2793
2794	is >> ch; // get the next lexeme
2795
2796	if (!is.good()) goto finish;
2797
2798	#ifdef BOOST_NO_STD_LOCALE
2799	cc = ch;
2800	#else
2801	cc = ct.narrow(ch, char());
2802	#endif /* BOOST_NO_STD_LOCALE */
2803
2804	if (cc == ')') // read "((a,b)"
2805	{
2806	is >> ch; // get the next lexeme
2807
2808	if (!is.good()) goto finish;
2809
2810	#ifdef BOOST_NO_STD_LOCALE
2811	cc = ch;
2812	#else
2813	cc = ct.narrow(ch, char());
2814	#endif /* BOOST_NO_STD_LOCALE */
2815
2816	if (cc == ')') // read "((a,b))"
2817	{
2818	o = octonion<T>(a,b);
2819	}
2820	else if (cc == ',') // read "((a,b),"
2821	{
2822	is >> ch; // get the next lexeme
2823
2824	if (!is.good()) goto finish;
2825
2826	#ifdef BOOST_NO_STD_LOCALE
2827	cc = ch;
2828	#else
2829	cc = ct.narrow(ch, char());
2830	#endif /* BOOST_NO_STD_LOCALE */
2831
2832	if (cc == '(') // read "((a,b),("
2833	{
2834	is >> ch; // get the next lexeme
2835
2836	if (!is.good()) goto finish;
2837
2838	#ifdef BOOST_NO_STD_LOCALE
2839	cc = ch;
2840	#else
2841	cc = ct.narrow(ch, char());
2842	#endif /* BOOST_NO_STD_LOCALE */
2843
2844	if (cc == '(') // read "((a,b),(("
2845	{
2846	p = ::boost::math::quaternion<T>(a,b);
2847
2848	is.putback(ch);
2849
2850	is.putback(ch); // we backtrack twice, with the same value
2851
2852	is >> q; // read "((a,b),q"
2853
2854	if (!is.good()) goto finish;
2855
2856	is >> ch; // get the next lexeme
2857
2858	if (!is.good()) goto finish;
2859
2860	#ifdef BOOST_NO_STD_LOCALE
2861	cc = ch;
2862	#else
2863	cc = ct.narrow(ch, char());
2864	#endif /* BOOST_NO_STD_LOCALE */
2865
2866	if (cc == ')') // read "((a,b),q)"
2867	{
2868	o = octonion<T>(p,q);
2869	}
2870	else // error
2871	{
2872	#if BOOST_WORKAROUND(__GNUC__, < 3)
2873	is.setstate(::std::ios::failbit);
2874	#else
2875	is.setstate(::std::ios_base::failbit);
2876	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2877	}
2878	}
2879	else // read "((a,b),(c" or "((a,b),(e"
2880	{
2881	is.putback(ch);
2882
2883	is >> c;
2884
2885	if (!is.good()) goto finish;
2886
2887	is >> ch; // get the next lexeme
2888
2889	if (!is.good()) goto finish;
2890
2891	#ifdef BOOST_NO_STD_LOCALE
2892	cc = ch;
2893	#else
2894	cc = ct.narrow(ch, char());
2895	#endif /* BOOST_NO_STD_LOCALE */
2896
2897	if (cc == ')') // read "((a,b),(c)" (ambiguity resolution)
2898	{
2899	is >> ch; // get the next lexeme
2900
2901	if (!is.good()) goto finish;
2902
2903	#ifdef BOOST_NO_STD_LOCALE
2904	cc = ch;
2905	#else
2906	cc = ct.narrow(ch, char());
2907	#endif /* BOOST_NO_STD_LOCALE */
2908
2909	if (cc == ')') // read "((a,b),(c))"
2910	{
2911	o = octonion<T>(a,b,c);
2912	}
2913	else if (cc == ',') // read "((a,b),(c),"
2914	{
2915	u = ::std::complex<T>(a,b);
2916
2917	v = ::std::complex<T>(c);
2918
2919	is >> x; // read "((a,b),(c),x"
2920
2921	if (!is.good()) goto finish;
2922
2923	is >> ch; // get the next lexeme
2924
2925	if (!is.good()) goto finish;
2926
2927	#ifdef BOOST_NO_STD_LOCALE
2928	cc = ch;
2929	#else
2930	cc = ct.narrow(ch, char());
2931	#endif /* BOOST_NO_STD_LOCALE */
2932
2933	if (cc == ')') // read "((a,b),(c),x)"
2934	{
2935	o = octonion<T>(u,v,x);
2936	}
2937	else if (cc == ',') // read "((a,b),(c),x,"
2938	{
2939	is >> y; // read "((a,b),(c),x,y"
2940
2941	if (!is.good()) goto finish;
2942
2943	is >> ch; // get the next lexeme
2944
2945	if (!is.good()) goto finish;
2946
2947	#ifdef BOOST_NO_STD_LOCALE
2948	cc = ch;
2949	#else
2950	cc = ct.narrow(ch, char());
2951	#endif /* BOOST_NO_STD_LOCALE */
2952
2953	if (cc == ')') // read "((a,b),(c),x,y)"
2954	{
2955	o = octonion<T>(u,v,x,y);
2956	}
2957	else // error
2958	{
2959	#if BOOST_WORKAROUND(__GNUC__, < 3)
2960	is.setstate(::std::ios::failbit);
2961	#else
2962	is.setstate(::std::ios_base::failbit);
2963	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2964	}
2965	}
2966	else // error
2967	{
2968	#if BOOST_WORKAROUND(__GNUC__, < 3)
2969	is.setstate(::std::ios::failbit);
2970	#else
2971	is.setstate(::std::ios_base::failbit);
2972	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2973	}
2974	}
2975	else // error
2976	{
2977	#if BOOST_WORKAROUND(__GNUC__, < 3)
2978	is.setstate(::std::ios::failbit);
2979	#else
2980	is.setstate(::std::ios_base::failbit);
2981	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2982	}
2983	}
2984	else if (cc == ',') // read "((a,b),(c," or "((a,b),(e,"
2985	{
2986	is >> ch; // get the next lexeme
2987
2988	if (!is.good()) goto finish;
2989
2990	#ifdef BOOST_NO_STD_LOCALE
2991	cc = ch;
2992	#else
2993	cc = ct.narrow(ch, char());
2994	#endif /* BOOST_NO_STD_LOCALE */
2995
2996	if (cc == '(') // read "((a,b),(e,(" (ambiguity resolution)
2997	{
2998	u = ::std::complex<T>(a,b);
2999
3000	x = ::std::complex<T>(c); // "c" is actually "e"
3001
3002	is.putback(ch);
3003
3004	is >> y; // read "((a,b),(e,y"
3005
3006	if (!is.good()) goto finish;
3007
3008	is >> ch; // get the next lexeme
3009
3010	if (!is.good()) goto finish;
3011
3012	#ifdef BOOST_NO_STD_LOCALE
3013	cc = ch;
3014	#else
3015	cc = ct.narrow(ch, char());
3016	#endif /* BOOST_NO_STD_LOCALE */
3017
3018	if (cc == ')') // read "((a,b),(e,y)"
3019	{
3020	is >> ch; // get the next lexeme
3021
3022	if (!is.good()) goto finish;
3023
3024	#ifdef BOOST_NO_STD_LOCALE
3025	cc = ch;
3026	#else
3027	cc = ct.narrow(ch, char());
3028	#endif /* BOOST_NO_STD_LOCALE */
3029
3030	if (cc == ')') // read "((a,b),(e,y))"
3031	{
3032	o = octonion<T>(u,v,x,y);
3033	}
3034	else // error
3035	{
3036	#if BOOST_WORKAROUND(__GNUC__, < 3)
3037	is.setstate(::std::ios::failbit);
3038	#else
3039	is.setstate(::std::ios_base::failbit);
3040	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3041	}
3042	}
3043	else // error
3044	{
3045	#if BOOST_WORKAROUND(__GNUC__, < 3)
3046	is.setstate(::std::ios::failbit);
3047	#else
3048	is.setstate(::std::ios_base::failbit);
3049	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3050	}
3051	}
3052	else // read "((a,b),(c,d" or "((a,b),(e,f"
3053	{
3054	is.putback(ch);
3055
3056	is >> d;
3057
3058	if (!is.good()) goto finish;
3059
3060	is >> ch; // get the next lexeme
3061
3062	if (!is.good()) goto finish;
3063
3064	#ifdef BOOST_NO_STD_LOCALE
3065	cc = ch;
3066	#else
3067	cc = ct.narrow(ch, char());
3068	#endif /* BOOST_NO_STD_LOCALE */
3069
3070	if (cc == ')') // read "((a,b),(c,d)" (ambiguity resolution)
3071	{
3072	u = ::std::complex<T>(a,b);
3073
3074	v = ::std::complex<T>(c,d);
3075
3076	is >> ch; // get the next lexeme
3077
3078	if (!is.good()) goto finish;
3079
3080	#ifdef BOOST_NO_STD_LOCALE
3081	cc = ch;
3082	#else
3083	cc = ct.narrow(ch, char());
3084	#endif /* BOOST_NO_STD_LOCALE */
3085
3086	if (cc == ')') // read "((a,b),(c,d))"
3087	{
3088	o = octonion<T>(u,v);
3089	}
3090	else if (cc == ',') // read "((a,b),(c,d),"
3091	{
3092	is >> x; // read "((a,b),(c,d),x
3093
3094	if (!is.good()) goto finish;
3095
3096	is >> ch; // get the next lexeme
3097
3098	if (!is.good()) goto finish;
3099
3100	#ifdef BOOST_NO_STD_LOCALE
3101	cc = ch;
3102	#else
3103	cc = ct.narrow(ch, char());
3104	#endif /* BOOST_NO_STD_LOCALE */
3105
3106	if (cc == ')') // read "((a,b),(c,d),x)"
3107	{
3108	o = octonion<T>(u,v,x);
3109	}
3110	else if (cc == ',') // read "((a,b),(c,d),x,"
3111	{
3112	is >> y; // read "((a,b),(c,d),x,y"
3113
3114	if (!is.good()) goto finish;
3115
3116	is >> ch; // get the next lexeme
3117
3118	if (!is.good()) goto finish;
3119
3120	#ifdef BOOST_NO_STD_LOCALE
3121	cc = ch;
3122	#else
3123	cc = ct.narrow(ch, char());
3124	#endif /* BOOST_NO_STD_LOCALE */
3125
3126	if (cc == ')') // read "((a,b),(c,d),x,y)"
3127	{
3128	o = octonion<T>(u,v,x,y);
3129	}
3130	else // error
3131	{
3132	#if BOOST_WORKAROUND(__GNUC__, < 3)
3133	is.setstate(::std::ios::failbit);
3134	#else
3135	is.setstate(::std::ios_base::failbit);
3136	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3137	}
3138	}
3139	else // error
3140	{
3141	#if BOOST_WORKAROUND(__GNUC__, < 3)
3142	is.setstate(::std::ios::failbit);
3143	#else
3144	is.setstate(::std::ios_base::failbit);
3145	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3146	}
3147	}
3148	else // error
3149	{
3150	#if BOOST_WORKAROUND(__GNUC__, < 3)
3151	is.setstate(::std::ios::failbit);
3152	#else
3153	is.setstate(::std::ios_base::failbit);
3154	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3155	}
3156	}
3157	else if (cc == ',') // read "((a,b),(e,f," (ambiguity resolution)
3158	{
3159	p = ::boost::math::quaternion<T>(a,b); // too late to backtrack
3160
3161	is >> g; // read "((a,b),(e,f,g"
3162
3163	if (!is.good()) goto finish;
3164
3165	is >> ch; // get the next lexeme
3166
3167	if (!is.good()) goto finish;
3168
3169	#ifdef BOOST_NO_STD_LOCALE
3170	cc = ch;
3171	#else
3172	cc = ct.narrow(ch, char());
3173	#endif /* BOOST_NO_STD_LOCALE */
3174
3175	if (cc == ')') // read "((a,b),(e,f,g)"
3176	{
3177	is >> ch; // get the next lexeme
3178
3179	if (!is.good()) goto finish;
3180
3181	#ifdef BOOST_NO_STD_LOCALE
3182	cc = ch;
3183	#else
3184	cc = ct.narrow(ch, char());
3185	#endif /* BOOST_NO_STD_LOCALE */
3186
3187	if (cc == ')') // read "((a,b),(e,f,g))"
3188	{
3189	q = ::boost::math::quaternion<T>(c,d,g); // "c" is actually "e" and "d" is actually "f"
3190
3191	o = octonion<T>(p,q);
3192	}
3193	else // error
3194	{
3195	#if BOOST_WORKAROUND(__GNUC__, < 3)
3196	is.setstate(::std::ios::failbit);
3197	#else
3198	is.setstate(::std::ios_base::failbit);
3199	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3200	}
3201	}
3202	else if (cc == ',') // read "((a,b),(e,f,g,"
3203	{
3204	is >> h; // read "((a,b),(e,f,g,h"
3205
3206	if (!is.good()) goto finish;
3207
3208	is >> ch; // get the next lexeme
3209
3210	if (!is.good()) goto finish;
3211
3212	#ifdef BOOST_NO_STD_LOCALE
3213	cc = ch;
3214	#else
3215	cc = ct.narrow(ch, char());
3216	#endif /* BOOST_NO_STD_LOCALE */
3217
3218	if (cc == ')') // read "((a,b),(e,f,g,h)"
3219	{
3220	is >> ch; // get the next lexeme
3221
3222	if (!is.good()) goto finish;
3223
3224	#ifdef BOOST_NO_STD_LOCALE
3225	cc = ch;
3226	#else
3227	cc = ct.narrow(ch, char());
3228	#endif /* BOOST_NO_STD_LOCALE */
3229
3230	if (cc == ')') // read ((a,b),(e,f,g,h))"
3231	{
3232	q = ::boost::math::quaternion<T>(c,d,g,h); // "c" is actually "e" and "d" is actually "f"
3233
3234	o = octonion<T>(p,q);
3235	}
3236	else // error
3237	{
3238	#if BOOST_WORKAROUND(__GNUC__, < 3)
3239	is.setstate(::std::ios::failbit);
3240	#else
3241	is.setstate(::std::ios_base::failbit);
3242	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3243	}
3244	}
3245	else // error
3246	{
3247	#if BOOST_WORKAROUND(__GNUC__, < 3)
3248	is.setstate(::std::ios::failbit);
3249	#else
3250	is.setstate(::std::ios_base::failbit);
3251	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3252	}
3253	}
3254	else // error
3255	{
3256	#if BOOST_WORKAROUND(__GNUC__, < 3)
3257	is.setstate(::std::ios::failbit);
3258	#else
3259	is.setstate(::std::ios_base::failbit);
3260	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3261	}
3262	}
3263	else // error
3264	{
3265	#if BOOST_WORKAROUND(__GNUC__, < 3)
3266	is.setstate(::std::ios::failbit);
3267	#else
3268	is.setstate(::std::ios_base::failbit);
3269	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3270	}
3271	}
3272	}
3273	else // error
3274	{
3275	#if BOOST_WORKAROUND(__GNUC__, < 3)
3276	is.setstate(::std::ios::failbit);
3277	#else
3278	is.setstate(::std::ios_base::failbit);
3279	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3280	}
3281	}
3282	}
3283	else // error
3284	{
3285	#if BOOST_WORKAROUND(__GNUC__, < 3)
3286	is.setstate(::std::ios::failbit);
3287	#else
3288	is.setstate(::std::ios_base::failbit);
3289	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3290	}
3291	}
3292	else // error
3293	{
3294	#if BOOST_WORKAROUND(__GNUC__, < 3)
3295	is.setstate(::std::ios::failbit);
3296	#else
3297	is.setstate(::std::ios_base::failbit);
3298	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3299	}
3300	}
3301	else if (cc == ',') // read "((a,b,"
3302	{
3303	is >> c; // read "((a,b,c"
3304
3305	if (!is.good()) goto finish;
3306
3307	is >> ch; // get the next lexeme
3308
3309	if (!is.good()) goto finish;
3310
3311	#ifdef BOOST_NO_STD_LOCALE
3312	cc = ch;
3313	#else
3314	cc = ct.narrow(ch, char());
3315	#endif /* BOOST_NO_STD_LOCALE */
3316
3317	if (cc == ')') // read "((a,b,c)"
3318	{
3319	is >> ch; // get the next lexeme
3320
3321	if (!is.good()) goto finish;
3322
3323	#ifdef BOOST_NO_STD_LOCALE
3324	cc = ch;
3325	#else
3326	cc = ct.narrow(ch, char());
3327	#endif /* BOOST_NO_STD_LOCALE */
3328
3329	if (cc == ')') // read "((a,b,c))"
3330	{
3331	o = octonion<T>(a,b,c);
3332	}
3333	else if (cc == ',') // read "((a,b,c),"
3334	{
3335	p = ::boost::math::quaternion<T>(a,b,c);
3336
3337	is >> q; // read "((a,b,c),q"
3338
3339	if (!is.good()) goto finish;
3340
3341	is >> ch; // get the next lexeme
3342
3343	if (!is.good()) goto finish;
3344
3345	#ifdef BOOST_NO_STD_LOCALE
3346	cc = ch;
3347	#else
3348	cc = ct.narrow(ch, char());
3349	#endif /* BOOST_NO_STD_LOCALE */
3350
3351	if (cc == ')') // read "((a,b,c),q)"
3352	{
3353	o = octonion<T>(p,q);
3354	}
3355	else // error
3356	{
3357	#if BOOST_WORKAROUND(__GNUC__, < 3)
3358	is.setstate(::std::ios::failbit);
3359	#else
3360	is.setstate(::std::ios_base::failbit);
3361	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3362	}
3363	}
3364	else // error
3365	{
3366	#if BOOST_WORKAROUND(__GNUC__, < 3)
3367	is.setstate(::std::ios::failbit);
3368	#else
3369	is.setstate(::std::ios_base::failbit);
3370	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3371	}
3372	}
3373	else if (cc == ',') // read "((a,b,c,"
3374	{
3375	is >> d; // read "((a,b,c,d"
3376
3377	if (!is.good()) goto finish;
3378
3379	is >> ch; // get the next lexeme
3380
3381	if (!is.good()) goto finish;
3382
3383	#ifdef BOOST_NO_STD_LOCALE
3384	cc = ch;
3385	#else
3386	cc = ct.narrow(ch, char());
3387	#endif /* BOOST_NO_STD_LOCALE */
3388
3389	if (cc == ')') // read "((a,b,c,d)"
3390	{
3391	is >> ch; // get the next lexeme
3392
3393	if (!is.good()) goto finish;
3394
3395	#ifdef BOOST_NO_STD_LOCALE
3396	cc = ch;
3397	#else
3398	cc = ct.narrow(ch, char());
3399	#endif /* BOOST_NO_STD_LOCALE */
3400
3401	if (cc == ')') // read "((a,b,c,d))"
3402	{
3403	o = octonion<T>(a,b,c,d);
3404	}
3405	else if (cc == ',') // read "((a,b,c,d),"
3406	{
3407	p = ::boost::math::quaternion<T>(a,b,c,d);
3408
3409	is >> q; // read "((a,b,c,d),q"
3410
3411	if (!is.good()) goto finish;
3412
3413	is >> ch; // get the next lexeme
3414
3415	if (!is.good()) goto finish;
3416
3417	#ifdef BOOST_NO_STD_LOCALE
3418	cc = ch;
3419	#else
3420	cc = ct.narrow(ch, char());
3421	#endif /* BOOST_NO_STD_LOCALE */
3422
3423	if (cc == ')') // read "((a,b,c,d),q)"
3424	{
3425	o = octonion<T>(p,q);
3426	}
3427	else // error
3428	{
3429	#if BOOST_WORKAROUND(__GNUC__, < 3)
3430	is.setstate(::std::ios::failbit);
3431	#else
3432	is.setstate(::std::ios_base::failbit);
3433	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3434	}
3435	}
3436	else // error
3437	{
3438	#if BOOST_WORKAROUND(__GNUC__, < 3)
3439	is.setstate(::std::ios::failbit);
3440	#else
3441	is.setstate(::std::ios_base::failbit);
3442	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3443	}
3444	}
3445	else // error
3446	{
3447	#if BOOST_WORKAROUND(__GNUC__, < 3)
3448	is.setstate(::std::ios::failbit);
3449	#else
3450	is.setstate(::std::ios_base::failbit);
3451	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3452	}
3453	}
3454	else // error
3455	{
3456	#if BOOST_WORKAROUND(__GNUC__, < 3)
3457	is.setstate(::std::ios::failbit);
3458	#else
3459	is.setstate(::std::ios_base::failbit);
3460	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3461	}
3462	}
3463	else // error
3464	{
3465	#if BOOST_WORKAROUND(__GNUC__, < 3)
3466	is.setstate(::std::ios::failbit);
3467	#else
3468	is.setstate(::std::ios_base::failbit);
3469	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3470	}
3471	}
3472	}
3473	else // error
3474	{
3475	#if BOOST_WORKAROUND(__GNUC__, < 3)
3476	is.setstate(::std::ios::failbit);
3477	#else
3478	is.setstate(::std::ios_base::failbit);
3479	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3480	}
3481	}
3482	}
3483	else // read "(a"
3484	{
3485	is.putback(ch);
3486
3487	is >> a; // we extract the first component
3488
3489	if (!is.good()) goto finish;
3490
3491	is >> ch; // get the next lexeme
3492
3493	if (!is.good()) goto finish;
3494
3495	#ifdef BOOST_NO_STD_LOCALE
3496	cc = ch;
3497	#else
3498	cc = ct.narrow(ch, char());
3499	#endif /* BOOST_NO_STD_LOCALE */
3500
3501	if (cc == ')') // read "(a)"
3502	{
3503	o = octonion<T>(a);
3504	}
3505	else if (cc == ',') // read "(a,"
3506	{
3507	is >> ch; // get the next lexeme
3508
3509	if (!is.good()) goto finish;
3510
3511	#ifdef BOOST_NO_STD_LOCALE
3512	cc = ch;
3513	#else
3514	cc = ct.narrow(ch, char());
3515	#endif /* BOOST_NO_STD_LOCALE */
3516
3517	if (cc == '(') // read "(a,("
3518	{
3519	is >> ch; // get the next lexeme
3520
3521	if (!is.good()) goto finish;
3522
3523	#ifdef BOOST_NO_STD_LOCALE
3524	cc = ch;
3525	#else
3526	cc = ct.narrow(ch, char());
3527	#endif /* BOOST_NO_STD_LOCALE */
3528
3529	if (cc == '(') // read "(a,(("
3530	{
3531	p = ::boost::math::quaternion<T>(a);
3532
3533	is.putback(ch);
3534
3535	is.putback(ch); // we backtrack twice, with the same value
3536
3537	is >> q; // read "(a,q"
3538
3539	if (!is.good()) goto finish;
3540
3541	is >> ch; // get the next lexeme
3542
3543	if (!is.good()) goto finish;
3544
3545	#ifdef BOOST_NO_STD_LOCALE
3546	cc = ch;
3547	#else
3548	cc = ct.narrow(ch, char());
3549	#endif /* BOOST_NO_STD_LOCALE */
3550
3551	if (cc == ')') // read "(a,q)"
3552	{
3553	o = octonion<T>(p,q);
3554	}
3555	else // error
3556	{
3557	#if BOOST_WORKAROUND(__GNUC__, < 3)
3558	is.setstate(::std::ios::failbit);
3559	#else
3560	is.setstate(::std::ios_base::failbit);
3561	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3562	}
3563	}
3564	else // read "(a,(c" or "(a,(e"
3565	{
3566	is.putback(ch);
3567
3568	is >> c;
3569
3570	if (!is.good()) goto finish;
3571
3572	is >> ch; // get the next lexeme
3573
3574	if (!is.good()) goto finish;
3575
3576	#ifdef BOOST_NO_STD_LOCALE
3577	cc = ch;
3578	#else
3579	cc = ct.narrow(ch, char());
3580	#endif /* BOOST_NO_STD_LOCALE */
3581
3582	if (cc == ')') // read "(a,(c)" (ambiguity resolution)
3583	{
3584	is >> ch; // get the next lexeme
3585
3586	if (!is.good()) goto finish;
3587
3588	#ifdef BOOST_NO_STD_LOCALE
3589	cc = ch;
3590	#else
3591	cc = ct.narrow(ch, char());
3592	#endif /* BOOST_NO_STD_LOCALE */
3593
3594	if (cc == ')') // read "(a,(c))"
3595	{
3596	o = octonion<T>(a,b,c);
3597	}
3598	else if (cc == ',') // read "(a,(c),"
3599	{
3600	u = ::std::complex<T>(a);
3601
3602	v = ::std::complex<T>(c);
3603
3604	is >> x; // read "(a,(c),x"
3605
3606	if (!is.good()) goto finish;
3607
3608	is >> ch; // get the next lexeme
3609
3610	if (!is.good()) goto finish;
3611
3612	#ifdef BOOST_NO_STD_LOCALE
3613	cc = ch;
3614	#else
3615	cc = ct.narrow(ch, char());
3616	#endif /* BOOST_NO_STD_LOCALE */
3617
3618	if (cc == ')') // read "(a,(c),x)"
3619	{
3620	o = octonion<T>(u,v,x);
3621	}
3622	else if (cc == ',') // read "(a,(c),x,"
3623	{
3624	is >> y; // read "(a,(c),x,y"
3625
3626	if (!is.good()) goto finish;
3627
3628	is >> ch; // get the next lexeme
3629
3630	if (!is.good()) goto finish;
3631
3632	#ifdef BOOST_NO_STD_LOCALE
3633	cc = ch;
3634	#else
3635	cc = ct.narrow(ch, char());
3636	#endif /* BOOST_NO_STD_LOCALE */
3637
3638	if (cc == ')') // read "(a,(c),x,y)"
3639	{
3640	o = octonion<T>(u,v,x,y);
3641	}
3642	else // error
3643	{
3644	#if BOOST_WORKAROUND(__GNUC__, < 3)
3645	is.setstate(::std::ios::failbit);
3646	#else
3647	is.setstate(::std::ios_base::failbit);
3648	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3649	}
3650	}
3651	else // error
3652	{
3653	#if BOOST_WORKAROUND(__GNUC__, < 3)
3654	is.setstate(::std::ios::failbit);
3655	#else
3656	is.setstate(::std::ios_base::failbit);
3657	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3658	}
3659	}
3660	else // error
3661	{
3662	#if BOOST_WORKAROUND(__GNUC__, < 3)
3663	is.setstate(::std::ios::failbit);
3664	#else
3665	is.setstate(::std::ios_base::failbit);
3666	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3667	}
3668	}
3669	else if (cc == ',') // read "(a,(c," or "(a,(e,"
3670	{
3671	is >> ch; // get the next lexeme
3672
3673	if (!is.good()) goto finish;
3674
3675	#ifdef BOOST_NO_STD_LOCALE
3676	cc = ch;
3677	#else
3678	cc = ct.narrow(ch, char());
3679	#endif /* BOOST_NO_STD_LOCALE */
3680
3681	if (cc == '(') // read "(a,(e,(" (ambiguity resolution)
3682	{
3683	u = ::std::complex<T>(a);
3684
3685	x = ::std::complex<T>(c); // "c" is actually "e"
3686
3687	is.putback(ch); // we backtrack
3688
3689	is >> y; // read "(a,(e,y"
3690
3691	if (!is.good()) goto finish;
3692
3693	is >> ch; // get the next lexeme
3694
3695	if (!is.good()) goto finish;
3696
3697	#ifdef BOOST_NO_STD_LOCALE
3698	cc = ch;
3699	#else
3700	cc = ct.narrow(ch, char());
3701	#endif /* BOOST_NO_STD_LOCALE */
3702
3703	if (cc == ')') // read "(a,(e,y)"
3704	{
3705	is >> ch; // get the next lexeme
3706
3707	if (!is.good()) goto finish;
3708
3709	#ifdef BOOST_NO_STD_LOCALE
3710	cc = ch;
3711	#else
3712	cc = ct.narrow(ch, char());
3713	#endif /* BOOST_NO_STD_LOCALE */
3714
3715	if (cc == ')') // read "(a,(e,y))"
3716	{
3717	o = octonion<T>(u,v,x,y);
3718	}
3719	else // error
3720	{
3721	#if BOOST_WORKAROUND(__GNUC__, < 3)
3722	is.setstate(::std::ios::failbit);
3723	#else
3724	is.setstate(::std::ios_base::failbit);
3725	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3726	}
3727	}
3728	else // error
3729	{
3730	#if BOOST_WORKAROUND(__GNUC__, < 3)
3731	is.setstate(::std::ios::failbit);
3732	#else
3733	is.setstate(::std::ios_base::failbit);
3734	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3735	}
3736	}
3737	else // read "(a,(c,d" or "(a,(e,f"
3738	{
3739	is.putback(ch);
3740
3741	is >> d;
3742
3743	if (!is.good()) goto finish;
3744
3745	is >> ch; // get the next lexeme
3746
3747	if (!is.good()) goto finish;
3748
3749	#ifdef BOOST_NO_STD_LOCALE
3750	cc = ch;
3751	#else
3752	cc = ct.narrow(ch, char());
3753	#endif /* BOOST_NO_STD_LOCALE */
3754
3755	if (cc == ')') // read "(a,(c,d)" (ambiguity resolution)
3756	{
3757	is >> ch; // get the next lexeme
3758
3759	if (!is.good()) goto finish;
3760
3761	#ifdef BOOST_NO_STD_LOCALE
3762	cc = ch;
3763	#else
3764	cc = ct.narrow(ch, char());
3765	#endif /* BOOST_NO_STD_LOCALE */
3766
3767	if (cc == ')') // read "(a,(c,d))"
3768	{
3769	o = octonion<T>(a,b,c,d);
3770	}
3771	else if (cc == ',') // read "(a,(c,d),"
3772	{
3773	u = ::std::complex<T>(a);
3774
3775	v = ::std::complex<T>(c,d);
3776
3777	is >> x; // read "(a,(c,d),x"
3778
3779	if (!is.good()) goto finish;
3780
3781	is >> ch; // get the next lexeme
3782
3783	if (!is.good()) goto finish;
3784
3785	#ifdef BOOST_NO_STD_LOCALE
3786	cc = ch;
3787	#else
3788	cc = ct.narrow(ch, char());
3789	#endif /* BOOST_NO_STD_LOCALE */
3790
3791	if (cc == ')') // read "(a,(c,d),x)"
3792	{
3793	o = octonion<T>(u,v,x);
3794	}
3795	else if (cc == ',') // read "(a,(c,d),x,"
3796	{
3797	is >> y; // read "(a,(c,d),x,y"
3798
3799	if (!is.good()) goto finish;
3800
3801	is >> ch; // get the next lexeme
3802
3803	if (!is.good()) goto finish;
3804
3805	#ifdef BOOST_NO_STD_LOCALE
3806	cc = ch;
3807	#else
3808	cc = ct.narrow(ch, char());
3809	#endif /* BOOST_NO_STD_LOCALE */
3810
3811	if (cc == ')') // read "(a,(c,d),x,y)"
3812	{
3813	o = octonion<T>(u,v,x,y);
3814	}
3815	else // error
3816	{
3817	#if BOOST_WORKAROUND(__GNUC__, < 3)
3818	is.setstate(::std::ios::failbit);
3819	#else
3820	is.setstate(::std::ios_base::failbit);
3821	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3822	}
3823	}
3824	else // error
3825	{
3826	#if BOOST_WORKAROUND(__GNUC__, < 3)
3827	is.setstate(::std::ios::failbit);
3828	#else
3829	is.setstate(::std::ios_base::failbit);
3830	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3831	}
3832	}
3833	else // error
3834	{
3835	#if BOOST_WORKAROUND(__GNUC__, < 3)
3836	is.setstate(::std::ios::failbit);
3837	#else
3838	is.setstate(::std::ios_base::failbit);
3839	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3840	}
3841	}
3842	else if (cc == ',') // read "(a,(e,f," (ambiguity resolution)
3843	{
3844	p = ::boost::math::quaternion<T>(a);
3845
3846	is >> g; // read "(a,(e,f,g"
3847
3848	if (!is.good()) goto finish;
3849
3850	is >> ch; // get the next lexeme
3851
3852	if (!is.good()) goto finish;
3853
3854	#ifdef BOOST_NO_STD_LOCALE
3855	cc = ch;
3856	#else
3857	cc = ct.narrow(ch, char());
3858	#endif /* BOOST_NO_STD_LOCALE */
3859
3860	if (cc == ')') // read "(a,(e,f,g)"
3861	{
3862	is >> ch; // get the next lexeme
3863
3864	if (!is.good()) goto finish;
3865
3866	#ifdef BOOST_NO_STD_LOCALE
3867	cc = ch;
3868	#else
3869	cc = ct.narrow(ch, char());
3870	#endif /* BOOST_NO_STD_LOCALE */
3871
3872	if (cc == ')') // read "(a,(e,f,g))"
3873	{
3874	q = ::boost::math::quaternion<T>(c,d,g); // "c" is actually "e" and "d" is actually "f"
3875
3876	o = octonion<T>(p,q);
3877	}
3878	else // error
3879	{
3880	#if BOOST_WORKAROUND(__GNUC__, < 3)
3881	is.setstate(::std::ios::failbit);
3882	#else
3883	is.setstate(::std::ios_base::failbit);
3884	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3885	}
3886	}
3887	else if (cc == ',') // read "(a,(e,f,g,"
3888	{
3889	is >> h; // read "(a,(e,f,g,h"
3890
3891	if (!is.good()) goto finish;
3892
3893	is >> ch; // get the next lexeme
3894
3895	if (!is.good()) goto finish;
3896
3897	#ifdef BOOST_NO_STD_LOCALE
3898	cc = ch;
3899	#else
3900	cc = ct.narrow(ch, char());
3901	#endif /* BOOST_NO_STD_LOCALE */
3902
3903	if (cc == ')') // read "(a,(e,f,g,h)"
3904	{
3905	is >> ch; // get the next lexeme
3906
3907	if (!is.good()) goto finish;
3908
3909	#ifdef BOOST_NO_STD_LOCALE
3910	cc = ch;
3911	#else
3912	cc = ct.narrow(ch, char());
3913	#endif /* BOOST_NO_STD_LOCALE */
3914
3915	if (cc == ')') // read "(a,(e,f,g,h))"
3916	{
3917	q = ::boost::math::quaternion<T>(c,d,g,h); // "c" is actually "e" and "d" is actually "f"
3918
3919	o = octonion<T>(p,q);
3920	}
3921	else // error
3922	{
3923	#if BOOST_WORKAROUND(__GNUC__, < 3)
3924	is.setstate(::std::ios::failbit);
3925	#else
3926	is.setstate(::std::ios_base::failbit);
3927	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3928	}
3929	}
3930	else // error
3931	{
3932	#if BOOST_WORKAROUND(__GNUC__, < 3)
3933	is.setstate(::std::ios::failbit);
3934	#else
3935	is.setstate(::std::ios_base::failbit);
3936	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3937	}
3938	}
3939	else // error
3940	{
3941	#if BOOST_WORKAROUND(__GNUC__, < 3)
3942	is.setstate(::std::ios::failbit);
3943	#else
3944	is.setstate(::std::ios_base::failbit);
3945	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3946	}
3947	}
3948	else // error
3949	{
3950	#if BOOST_WORKAROUND(__GNUC__, < 3)
3951	is.setstate(::std::ios::failbit);
3952	#else
3953	is.setstate(::std::ios_base::failbit);
3954	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3955	}
3956	}
3957	}
3958	else // error
3959	{
3960	#if BOOST_WORKAROUND(__GNUC__, < 3)
3961	is.setstate(::std::ios::failbit);
3962	#else
3963	is.setstate(::std::ios_base::failbit);
3964	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3965	}
3966	}
3967	}
3968	else // read "(a,b" or "(a,c" (ambiguity resolution)
3969	{
3970	is.putback(ch);
3971
3972	is >> b;
3973
3974	if (!is.good()) goto finish;
3975
3976	is >> ch; // get the next lexeme
3977
3978	if (!is.good()) goto finish;
3979
3980	#ifdef BOOST_NO_STD_LOCALE
3981	cc = ch;
3982	#else
3983	cc = ct.narrow(ch, char());
3984	#endif /* BOOST_NO_STD_LOCALE */
3985
3986	if (cc == ')') // read "(a,b)" (ambiguity resolution)
3987	{
3988	o = octonion<T>(a,b);
3989	}
3990	else if (cc == ',') // read "(a,b," or "(a,c,"
3991	{
3992	is >> ch; // get the next lexeme
3993
3994	if (!is.good()) goto finish;
3995
3996	#ifdef BOOST_NO_STD_LOCALE
3997	cc = ch;
3998	#else
3999	cc = ct.narrow(ch, char());
4000	#endif /* BOOST_NO_STD_LOCALE */
4001
4002	if (cc == '(') // read "(a,c,(" (ambiguity resolution)
4003	{
4004	u = ::std::complex<T>(a);
4005
4006	v = ::std::complex<T>(b); // "b" is actually "c"
4007
4008	is.putback(ch); // we backtrack
4009
4010	is >> x; // read "(a,c,x"
4011
4012	if (!is.good()) goto finish;
4013
4014	is >> ch; // get the next lexeme
4015
4016	if (!is.good()) goto finish;
4017
4018	#ifdef BOOST_NO_STD_LOCALE
4019	cc = ch;
4020	#else
4021	cc = ct.narrow(ch, char());
4022	#endif /* BOOST_NO_STD_LOCALE */
4023
4024	if (cc == ')') // read "(a,c,x)"
4025	{
4026	o = octonion<T>(u,v,x);
4027	}
4028	else if (cc == ',') // read "(a,c,x,"
4029	{
4030	is >> y; // read "(a,c,x,y" // read "(a,c,x"
4031
4032	if (!is.good()) goto finish;
4033
4034	is >> ch; // get the next lexeme
4035
4036	if (!is.good()) goto finish;
4037
4038	#ifdef BOOST_NO_STD_LOCALE
4039	cc = ch;
4040	#else
4041	cc = ct.narrow(ch, char());
4042	#endif /* BOOST_NO_STD_LOCALE */
4043
4044	if (cc == ')') // read "(a,c,x,y)"
4045	{
4046	o = octonion<T>(u,v,x,y);
4047	}
4048	else // error
4049	{
4050	#if BOOST_WORKAROUND(__GNUC__, < 3)
4051	is.setstate(::std::ios::failbit);
4052	#else
4053	is.setstate(::std::ios_base::failbit);
4054	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4055	}
4056	}
4057	else // error
4058	{
4059	#if BOOST_WORKAROUND(__GNUC__, < 3)
4060	is.setstate(::std::ios::failbit);
4061	#else
4062	is.setstate(::std::ios_base::failbit);
4063	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4064	}
4065	}
4066	else // read "(a,b,c" or "(a,c,e"
4067	{
4068	is.putback(ch);
4069
4070	is >> c;
4071
4072	if (!is.good()) goto finish;
4073
4074	is >> ch; // get the next lexeme
4075
4076	if (!is.good()) goto finish;
4077
4078	#ifdef BOOST_NO_STD_LOCALE
4079	cc = ch;
4080	#else
4081	cc = ct.narrow(ch, char());
4082	#endif /* BOOST_NO_STD_LOCALE */
4083
4084	if (cc == ')') // read "(a,b,c)" (ambiguity resolution)
4085	{
4086	o = octonion<T>(a,b,c);
4087	}
4088	else if (cc == ',') // read "(a,b,c," or "(a,c,e,"
4089	{
4090	is >> ch; // get the next lexeme
4091
4092	if (!is.good()) goto finish;
4093
4094	#ifdef BOOST_NO_STD_LOCALE
4095	cc = ch;
4096	#else
4097	cc = ct.narrow(ch, char());
4098	#endif /* BOOST_NO_STD_LOCALE */
4099
4100	if (cc == '(') // read "(a,c,e,(") (ambiguity resolution)
4101	{
4102	u = ::std::complex<T>(a);
4103
4104	v = ::std::complex<T>(b); // "b" is actually "c"
4105
4106	x = ::std::complex<T>(c); // "c" is actually "e"
4107
4108	is.putback(ch); // we backtrack
4109
4110	is >> y; // read "(a,c,e,y"
4111
4112	if (!is.good()) goto finish;
4113
4114	is >> ch; // get the next lexeme
4115
4116	if (!is.good()) goto finish;
4117
4118	#ifdef BOOST_NO_STD_LOCALE
4119	cc = ch;
4120	#else
4121	cc = ct.narrow(ch, char());
4122	#endif /* BOOST_NO_STD_LOCALE */
4123
4124	if (cc == ')') // read "(a,c,e,y)"
4125	{
4126	o = octonion<T>(u,v,x,y);
4127	}
4128	else // error
4129	{
4130	#if BOOST_WORKAROUND(__GNUC__, < 3)
4131	is.setstate(::std::ios::failbit);
4132	#else
4133	is.setstate(::std::ios_base::failbit);
4134	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4135	}
4136	}
4137	else // read "(a,b,c,d" (ambiguity resolution)
4138	{
4139	is.putback(ch); // we backtrack
4140
4141	is >> d;
4142
4143	if (!is.good()) goto finish;
4144
4145	is >> ch; // get the next lexeme
4146
4147	if (!is.good()) goto finish;
4148
4149	#ifdef BOOST_NO_STD_LOCALE
4150	cc = ch;
4151	#else
4152	cc = ct.narrow(ch, char());
4153	#endif /* BOOST_NO_STD_LOCALE */
4154
4155	if (cc == ')') // read "(a,b,c,d)"
4156	{
4157	o = octonion<T>(a,b,c,d);
4158	}
4159	else if (cc == ',') // read "(a,b,c,d,"
4160	{
4161	is >> e; // read "(a,b,c,d,e"
4162
4163	if (!is.good()) goto finish;
4164
4165	is >> ch; // get the next lexeme
4166
4167	if (!is.good()) goto finish;
4168
4169	#ifdef BOOST_NO_STD_LOCALE
4170	cc = ch;
4171	#else
4172	cc = ct.narrow(ch, char());
4173	#endif /* BOOST_NO_STD_LOCALE */
4174
4175	if (cc == ')') // read "(a,b,c,d,e)"
4176	{
4177	o = octonion<T>(a,b,c,d,e);
4178	}
4179	else if (cc == ',') // read "(a,b,c,d,e,"
4180	{
4181	is >> f; // read "(a,b,c,d,e,f"
4182
4183	if (!is.good()) goto finish;
4184
4185	is >> ch; // get the next lexeme
4186
4187	if (!is.good()) goto finish;
4188
4189	#ifdef BOOST_NO_STD_LOCALE
4190	cc = ch;
4191	#else
4192	cc = ct.narrow(ch, char());
4193	#endif /* BOOST_NO_STD_LOCALE */
4194
4195	if (cc == ')') // read "(a,b,c,d,e,f)"
4196	{
4197	o = octonion<T>(a,b,c,d,e,f);
4198	}
4199	else if (cc == ',') // read "(a,b,c,d,e,f,"
4200	{
4201	is >> g; // read "(a,b,c,d,e,f,g" // read "(a,b,c,d,e,f"
4202
4203	if (!is.good()) goto finish;
4204
4205	is >> ch; // get the next lexeme
4206
4207	if (!is.good()) goto finish;
4208
4209	#ifdef BOOST_NO_STD_LOCALE
4210	cc = ch;
4211	#else
4212	cc = ct.narrow(ch, char());
4213	#endif /* BOOST_NO_STD_LOCALE */
4214
4215	if (cc == ')') // read "(a,b,c,d,e,f,g)"
4216	{
4217	o = octonion<T>(a,b,c,d,e,f,g);
4218	}
4219	else if (cc == ',') // read "(a,b,c,d,e,f,g,"
4220	{
4221	is >> h; // read "(a,b,c,d,e,f,g,h" // read "(a,b,c,d,e,f,g" // read "(a,b,c,d,e,f"
4222
4223	if (!is.good()) goto finish;
4224
4225	is >> ch; // get the next lexeme
4226
4227	if (!is.good()) goto finish;
4228
4229	#ifdef BOOST_NO_STD_LOCALE
4230	cc = ch;
4231	#else
4232	cc = ct.narrow(ch, char());
4233	#endif /* BOOST_NO_STD_LOCALE */
4234
4235	if (cc == ')') // read "(a,b,c,d,e,f,g,h)"
4236	{
4237	o = octonion<T>(a,b,c,d,e,f,g,h);
4238	}
4239	else // error
4240	{
4241	#if BOOST_WORKAROUND(__GNUC__, < 3)
4242	is.setstate(::std::ios::failbit);
4243	#else
4244	is.setstate(::std::ios_base::failbit);
4245	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4246	}
4247	}
4248	else // error
4249	{
4250	#if BOOST_WORKAROUND(__GNUC__, < 3)
4251	is.setstate(::std::ios::failbit);
4252	#else
4253	is.setstate(::std::ios_base::failbit);
4254	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4255	}
4256	}
4257	else // error
4258	{
4259	#if BOOST_WORKAROUND(__GNUC__, < 3)
4260	is.setstate(::std::ios::failbit);
4261	#else
4262	is.setstate(::std::ios_base::failbit);
4263	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4264	}
4265	}
4266	else // error
4267	{
4268	#if BOOST_WORKAROUND(__GNUC__, < 3)
4269	is.setstate(::std::ios::failbit);
4270	#else
4271	is.setstate(::std::ios_base::failbit);
4272	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4273	}
4274	}
4275	else // error
4276	{
4277	#if BOOST_WORKAROUND(__GNUC__, < 3)
4278	is.setstate(::std::ios::failbit);
4279	#else
4280	is.setstate(::std::ios_base::failbit);
4281	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4282	}
4283	}
4284	}
4285	else // error
4286	{
4287	#if BOOST_WORKAROUND(__GNUC__, < 3)
4288	is.setstate(::std::ios::failbit);
4289	#else
4290	is.setstate(::std::ios_base::failbit);
4291	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4292	}
4293	}
4294	}
4295	else // error
4296	{
4297	#if BOOST_WORKAROUND(__GNUC__, < 3)
4298	is.setstate(::std::ios::failbit);
4299	#else
4300	is.setstate(::std::ios_base::failbit);
4301	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4302	}
4303	}
4304	}
4305	else // error
4306	{
4307	#if BOOST_WORKAROUND(__GNUC__, < 3)
4308	is.setstate(::std::ios::failbit);
4309	#else
4310	is.setstate(::std::ios_base::failbit);
4311	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4312	}
4313	}
4314	}
4315	else // format: a
4316	{
4317	is.putback(ch);
4318
4319	is >> a; // we extract the first component
4320
4321	if (!is.good()) goto finish;
4322
4323	o = octonion<T>(a);
4324	}
4325
4326	finish:
4327	return(is);
4328	}
4329
4330
4331	#if BOOST_WORKAROUND(__GNUC__, < 3)
4332	template<typename T>
4333	::std::ostream & operator << ( ::std::ostream & os,
4334	octonion<T> const & o)
4335	#else
4336	template<typename T, typename charT, class traits>
4337	::std::basic_ostream<charT,traits> & operator << ( ::std::basic_ostream<charT,traits> & os,
4338	octonion<T> const & o)
4339	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4340	{
4341	#if BOOST_WORKAROUND(__GNUC__, < 3)
4342	::std::ostringstream s;
4343	#else
4344	::std::basic_ostringstream<charT,traits> s;
4345	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4346
4347	s.flags(os.flags());
4348	#ifdef BOOST_NO_STD_LOCALE
4349	#else
4350	s.imbue(os.getloc());
4351	#endif /* BOOST_NO_STD_LOCALE */
4352	s.precision(os.precision());
4353
4354	s << '(' << o.R_component_1() << ','
4355	<< o.R_component_2() << ','
4356	<< o.R_component_3() << ','
4357	<< o.R_component_4() << ','
4358	<< o.R_component_5() << ','
4359	<< o.R_component_6() << ','
4360	<< o.R_component_7() << ','
4361	<< o.R_component_8() << ')';
4362
4363	return os << s.str();
4364	}
4365
4366
4367	// values
4368
4369	template<typename T>
4370	inline T real(octonion<T> const & o)
4371	{
4372	return(o.real());
4373	}
4374
4375
4376	template<typename T>
4377	inline octonion<T> unreal(octonion<T> const & o)
4378	{
4379	return(o.unreal());
4380	}
4381
4382
4383	#define BOOST_OCTONION_VALARRAY_LOADER \
4384	using ::std::valarray; \
4385	\
4386	valarray<T> temp(8); \
4387	\
4388	temp[0] = o.R_component_1(); \
4389	temp[1] = o.R_component_2(); \
4390	temp[2] = o.R_component_3(); \
4391	temp[3] = o.R_component_4(); \
4392	temp[4] = o.R_component_5(); \
4393	temp[5] = o.R_component_6(); \
4394	temp[6] = o.R_component_7(); \
4395	temp[7] = o.R_component_8();
4396
4397
4398	template<typename T>
4399	inline T sup(octonion<T> const & o)
4400	{
4401	#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
4402	using ::std::abs;
4403	#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
4404
4405	BOOST_OCTONION_VALARRAY_LOADER
4406
4407	#if BOOST_WORKAROUND(__GNUC__, < 3)
4408	return((BOOST_GET_VALARRAY(T, abs(temp)).max)());
4409	#else
4410	return((abs(temp).max)());
4411	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4412	}
4413
4414
4415	template<typename T>
4416	inline T l1(octonion<T> const & o)
4417	{
4418	#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
4419	using ::std::abs;
4420	#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
4421
4422	BOOST_OCTONION_VALARRAY_LOADER
4423
4424	#if BOOST_WORKAROUND(__GNUC__, < 3)
4425	return(BOOST_GET_VALARRAY(T, abs(temp)).sum());
4426	#else
4427	return(abs(temp).sum());
4428	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4429	}
4430
4431
4432	template<typename T>
4433	inline T abs(const octonion<T> & o)
4434	{
4435	#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
4436	using ::std::abs;
4437	#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
4438
4439	using ::std::sqrt;
4440
4441	BOOST_OCTONION_VALARRAY_LOADER
4442
4443	#if BOOST_WORKAROUND(__GNUC__, < 3)
4444	T maxim = (BOOST_GET_VALARRAY(T,abs(temp)).max)(); // overflow protection
4445	#else
4446	T maxim = (abs(temp).max)(); // overflow protection
4447	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4448
4449	if (maxim == static_cast<T>(0))
4450	{
4451	return(maxim);
4452	}
4453	else
4454	{
4455	T mixam = static_cast<T>(1)/maxim; // prefer multiplications over divisions
4456
4457	temp *= mixam;
4458
4459	temp *= temp;
4460
4461	return(maxim*sqrt(temp.sum()));
4462	}
4463
4464	//return(::std::sqrt(norm(o)));
4465	}
4466
4467
4468	#undef BOOST_OCTONION_VALARRAY_LOADER
4469
4470
4471	// Note: This is the Cayley norm, not the Euclidian norm...
4472
4473	template<typename T>
4474	inline T norm(octonion<T> const & o)
4475	{
4476	return(real(o*conj(o)));
4477	}
4478
4479
4480	template<typename T>
4481	inline octonion<T> conj(octonion<T> const & o)
4482	{
4483	return(octonion<T>( +o.R_component_1(),
4484	-o.R_component_2(),
4485	-o.R_component_3(),
4486	-o.R_component_4(),
4487	-o.R_component_5(),
4488	-o.R_component_6(),
4489	-o.R_component_7(),
4490	-o.R_component_8()));
4491	}
4492
4493
4494	// Note: There is little point, for the octonions, to introduce the equivalents
4495	// to the complex "arg" and the quaternionic "cylindropolar".
4496
4497
4498	template<typename T>
4499	inline octonion<T> spherical(T const & rho,
4500	T const & theta,
4501	T const & phi1,
4502	T const & phi2,
4503	T const & phi3,
4504	T const & phi4,
4505	T const & phi5,
4506	T const & phi6)
4507	{
4508	using ::std::cos;
4509	using ::std::sin;
4510
4511	//T a = cos(theta)cos(phi1)cos(phi2)cos(phi3)cos(phi4)cos(phi5)cos(phi6);
4512	//T b = sin(theta)cos(phi1)cos(phi2)cos(phi3)cos(phi4)cos(phi5)cos(phi6);
4513	//T c = sin(phi1)cos(phi2)cos(phi3)cos(phi4)cos(phi5)*cos(phi6);
4514	//T d = sin(phi2)cos(phi3)cos(phi4)cos(phi5)cos(phi6);
4515	//T e = sin(phi3)cos(phi4)cos(phi5)*cos(phi6);
4516	//T f = sin(phi4)cos(phi5)cos(phi6);
4517	//T g = sin(phi5)*cos(phi6);
4518	//T h = sin(phi6);
4519
4520	T courrant = static_cast<T>(1);
4521
4522	T h = sin(phi6);
4523
4524	courrant *= cos(phi6);
4525
4526	T g = sin(phi5)*courrant;
4527
4528	courrant *= cos(phi5);
4529
4530	T f = sin(phi4)*courrant;
4531
4532	courrant *= cos(phi4);
4533
4534	T e = sin(phi3)*courrant;
4535
4536	courrant *= cos(phi3);
4537
4538	T d = sin(phi2)*courrant;
4539
4540	courrant *= cos(phi2);
4541
4542	T c = sin(phi1)*courrant;
4543
4544	courrant *= cos(phi1);
4545
4546	T b = sin(theta)*courrant;
4547	T a = cos(theta)*courrant;
4548
4549	return(rho*octonion<T>(a,b,c,d,e,f,g,h));
4550	}
4551
4552
4553	template<typename T>
4554	inline octonion<T> multipolar(T const & rho1,
4555	T const & theta1,
4556	T const & rho2,
4557	T const & theta2,
4558	T const & rho3,
4559	T const & theta3,
4560	T const & rho4,
4561	T const & theta4)
4562	{
4563	using ::std::cos;
4564	using ::std::sin;
4565
4566	T a = rho1*cos(theta1);
4567	T b = rho1*sin(theta1);
4568	T c = rho2*cos(theta2);
4569	T d = rho2*sin(theta2);
4570	T e = rho3*cos(theta3);
4571	T f = rho3*sin(theta3);
4572	T g = rho4*cos(theta4);
4573	T h = rho4*sin(theta4);
4574
4575	return(octonion<T>(a,b,c,d,e,f,g,h));
4576	}
4577
4578
4579	template<typename T>
4580	inline octonion<T> cylindrical(T const & r,
4581	T const & angle,
4582	T const & h1,
4583	T const & h2,
4584	T const & h3,
4585	T const & h4,
4586	T const & h5,
4587	T const & h6)
4588	{
4589	using ::std::cos;
4590	using ::std::sin;
4591
4592	T a = r*cos(angle);
4593	T b = r*sin(angle);
4594
4595	return(octonion<T>(a,b,h1,h2,h3,h4,h5,h6));
4596	}
4597
4598
4599	template<typename T>
4600	inline octonion<T> exp(octonion<T> const & o)
4601	{
4602	using ::std::exp;
4603	using ::std::cos;
4604
4605	using ::boost::math::sinc_pi;
4606
4607	T u = exp(real(o));
4608
4609	T z = abs(unreal(o));
4610
4611	T w = sinc_pi(z);
4612
4613	return(u*octonion<T>(cos(z),
4614	wo.R_component_2(), wo.R_component_3(),
4615	wo.R_component_4(), wo.R_component_5(),
4616	wo.R_component_6(), wo.R_component_7(),
4617	w*o.R_component_8()));
4618	}
4619
4620
4621	template<typename T>
4622	inline octonion<T> cos(octonion<T> const & o)
4623	{
4624	using ::std::sin;
4625	using ::std::cos;
4626	using ::std::cosh;
4627
4628	using ::boost::math::sinhc_pi;
4629
4630	T z = abs(unreal(o));
4631
4632	T w = -sin(o.real())*sinhc_pi(z);
4633
4634	return(octonion<T>(cos(o.real())*cosh(z),
4635	wo.R_component_2(), wo.R_component_3(),
4636	wo.R_component_4(), wo.R_component_5(),
4637	wo.R_component_6(), wo.R_component_7(),
4638	w*o.R_component_8()));
4639	}
4640
4641
4642	template<typename T>
4643	inline octonion<T> sin(octonion<T> const & o)
4644	{
4645	using ::std::sin;
4646	using ::std::cos;
4647	using ::std::cosh;
4648
4649	using ::boost::math::sinhc_pi;
4650
4651	T z = abs(unreal(o));
4652
4653	T w = +cos(o.real())*sinhc_pi(z);
4654
4655	return(octonion<T>(sin(o.real())*cosh(z),
4656	wo.R_component_2(), wo.R_component_3(),
4657	wo.R_component_4(), wo.R_component_5(),
4658	wo.R_component_6(), wo.R_component_7(),
4659	w*o.R_component_8()));
4660	}
4661
4662
4663	template<typename T>
4664	inline octonion<T> tan(octonion<T> const & o)
4665	{
4666	return(sin(o)/cos(o));
4667	}
4668
4669
4670	template<typename T>
4671	inline octonion<T> cosh(octonion<T> const & o)
4672	{
4673	return((exp(+o)+exp(-o))/static_cast<T>(2));
4674	}
4675
4676
4677	template<typename T>
4678	inline octonion<T> sinh(octonion<T> const & o)
4679	{
4680	return((exp(+o)-exp(-o))/static_cast<T>(2));
4681	}
4682
4683
4684	template<typename T>
4685	inline octonion<T> tanh(octonion<T> const & o)
4686	{
4687	return(sinh(o)/cosh(o));
4688	}
4689
4690
4691	template<typename T>
4692	octonion<T> pow(octonion<T> const & o,
4693	int n)
4694	{
4695	if (n > 1)
4696	{
4697	int m = n>>1;
4698
4699	octonion<T> result = pow(o, m);
4700
4701	result *= result;
4702
4703	if (n != (m<<1))
4704	{
4705	result *= o; // n odd
4706	}
4707
4708	return(result);
4709	}
4710	else if (n == 1)
4711	{
4712	return(o);
4713	}
4714	else if (n == 0)
4715	{
4716	return(octonion<T>(1));
4717	}
4718	else /* n < 0 */
4719	{
4720	return(pow(octonion<T>(1)/o,-n));
4721	}
4722	}
4723
4724
4725	// helper templates for converting copy constructors (definition)
4726
4727	namespace detail
4728	{
4729
4730	template< typename T,
4731	typename U
4732	>
4733	octonion<T> octonion_type_converter(octonion<U> const & rhs)
4734	{
4735	return(octonion<T>( static_cast<T>(rhs.R_component_1()),
4736	static_cast<T>(rhs.R_component_2()),
4737	static_cast<T>(rhs.R_component_3()),
4738	static_cast<T>(rhs.R_component_4()),
4739	static_cast<T>(rhs.R_component_5()),
4740	static_cast<T>(rhs.R_component_6()),
4741	static_cast<T>(rhs.R_component_7()),
4742	static_cast<T>(rhs.R_component_8())));
4743	}
4744	}
4745	}
4746	}
4747
4748
4749	#if BOOST_WORKAROUND(__GNUC__, < 3)
4750	#undef BOOST_GET_VALARRAY
4751	#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4752
4753
4754	#endif /* BOOST_OCTONION_HPP */

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